May the Lord abundantly bless you.
Yes, they rejected the sign so He did not have to take back the healing.
If it would have caused them to believe in Jesus, the man may not have been healed in the first place (except that he had personal faith to be healed); because it would have been a sign given to a wicked and adulterous generation.
Jesus did say to the man "Sin no more, lest a worse thing come upon you".
And we do not hear that the man continued to be healed after he "betrayed" Jesus...
The last we hear of the man is in the very story that we first hear of him in.
Nevertheless, Jesus did not have to take back the miracle; because the man was not wicked and adulterous. The Pharisees were the established religion of the day; and in telling them that Jesus had healed him, maybe he just wanted God to get the glory. It wasn't his fault that the Pharisees persecuted Jesus as a result.
Because, notice it doesn't say that he told them that it was Jesus who told him to take up his bed and walk. He specifically said that Jesus had healed him. That is something you or I might do if we wanted Jesus to get the glory for the miracle.
Jesus is God the Son, He knows the future. For example, that the cock would crow when Peter thrice denied Him.
Jesus planned this, went out of His way to find this person, ignoring other sick people there. Then He commands the man to "take up his bed and walk" so the Jews would object.
Then Jesus finds Him again, reveals His identity. Tells him "sin no more" knowing that is precisely what the "rat" will do:
14 Afterward Jesus found him in the temple, and said to him, "See, you have been made well. Sin no more, lest a worse thing come upon you."
15 The man departed and told the Jews that it was Jesus who had made him well. (Jn. 5:14-15 NKJ)
Jesus wanted this opportunity to confront the religious authorities with precisely the message He did:
8 Jesus said to him, "Rise, take up your bed and walk."
9 And immediately the man was made well, took up his bed, and walked. And that day was the Sabbath.
10 The Jews therefore said to him who was cured, "It is the Sabbath; it is not lawful for you to carry your bed."
11 He answered them, "He who made me well said to me,`Take up your bed and walk.'"
12 Then they asked him, "Who is the Man who said to you,`Take up your bed and walk '?"
13 But the one who was healed did not know who it was, for Jesus had withdrawn, a multitude being in that place.
14 Afterward Jesus found him in the temple, and said to him, "See, you have been made well. Sin no more, lest a worse thing come upon you."
15 The man departed and told the Jews that it was Jesus who had made him well.
16 For this reason the Jews persecuted Jesus, and sought to kill Him, because He had done these things on the Sabbath.
17 But Jesus answered them, "My Father has been working until now, and I have been working."
18 Therefore the Jews sought all the more to kill Him, because He not only broke the Sabbath, but also said that God was His Father, making Himself equal with God.
19 Then Jesus answered and said to them, "Most assuredly, I say to you, the Son can do nothing of Himself, but what He sees the Father do; for whatever He does, the Son also does in like manner.
20 "For the Father loves the Son, and shows Him all things that He Himself does; and He will show Him greater works than these, that you may marvel.
21 "For as the Father raises the dead and gives life to them, even so the Son gives life to whom He will.
22 "For the Father judges no one, but has committed all judgment to the Son,
23 "that all should honor the Son just as they honor the Father. He who does not honor the Son does not honor the Father who sent Him.
24 "Most assuredly, I say to you, he who hears My word and believes in Him who sent Me has everlasting life, and shall not come into judgment, but has passed from death into life.
25 "Most assuredly, I say to you, the hour is coming, and now is, when the dead will hear the voice of the Son of God; and those who hear will live.
26 "For as the Father has life in Himself, so He has granted the Son to have life in Himself,
27 "and has given Him authority to execute judgment also, because He is the Son of Man.
28 "Do not marvel at this; for the hour is coming in which all who are in the graves will hear His voice
29 "and come forth-- those who have done good, to the resurrection of life, and those who have done evil, to the resurrection of condemnation.
30 "I can of Myself do nothing. As I hear, I judge; and My judgment is righteous, because I do not seek My own will but the will of the Father who sent Me.
31 "If I bear witness of Myself, My witness is not true.
32 "There is another who bears witness of Me, and I know that the witness which He witnesses of Me is true.
33 "You have sent to John, and he has borne witness to the truth.
34 "Yet I do not receive testimony from man, but I say these things that you may be saved.
35 "He was the burning and shining lamp, and you were willing for a time to rejoice in his light.
36 "But I have a greater witness than John's; for the works which the Father has given Me to finish-- the very works that I do-- bear witness of Me, that the Father has sent Me.
37 "And the Father Himself, who sent Me, has testified of Me. You have neither heard His voice at any time, nor seen His form.
38 "But you do not have His word abiding in you, because whom He sent, Him you do not believe.
39 "You search the Scriptures, for in them you think you have eternal life; and these are they which testify of Me.
40 "But you are not willing to come to Me that you may have life.
41 "I do not receive honor from men.
42 "But I know you, that you do not have the love of God in you.
43 "I have come in My Father's name, and you do not receive Me; if another comes in his own name, him you will receive.
44 "How can you believe, who receive honor from one another, and do not seek the honor that comes from the only God?
45 "Do not think that I shall accuse you to the Father; there is one who accuses you-- Moses, in whom you trust.
46 "For if you believed Moses, you would believe Me; for he wrote about Me.
47 "But if you do not believe his writings, how will you believe My words?" (Jn. 5:8-6:1 NKJ)
Even though the man betrayed Christ, given His command we are to love our enemies, its impossible Jesus took back the healing. He practiced what He preached.