He tried to make a condition

Amr had spent years working against the Muslims. He had gone to Abyssinia to have the emigrants extradited. He had been on the other side of it for about as long as there had been a side to be on.

When he came to Madinah to accept Islam, he put out his hand to give the pledge — and then pulled it back.

He was asked what the matter was.

He said he wanted to make a condition. Asked what condition, he said: that I be forgiven.

That is the whole of the episode, and it is worth sitting with what it reveals. This is a capable, senior man, negotiating at the last moment of a decision he has already made. And what he is trying to negotiate for is not standing, or command, or any of the things he could plausibly have asked for. It is that the previous twenty years should not count against him.

The answer he was given is the reason the report is remembered: did you not know that Islam demolishes what came before it?

He had been afraid of a debt that had already been cancelled.

The account is in Sahih Muslim, narrated by Amr himself. That matters — it is not a story told about him by someone else. He is the one who chose to report that he hesitated, and why.