You can’t talk a reputation back. You can only act it back, slowly.

Reputation is other people’s prediction of what you will do next, and predictions update on evidence, not on argument. Explaining why they should think better of you asks them to overwrite what they saw with what you say, which nobody does. Repeated behaviour over weeks is the only input strong enough to move it.

Pick the one thing people doubt about you and be boringly reliable about it for a month. On time, every time, with no commentary. Do not point it out. Let somebody else be the one who notices.