There isn't a reassign feature for Gift Aid Declaration.
You would first need to Reverse any Gift Aid claimed on the incorrect Constituent's donations and ensure this is repaid prior to completing the next part.
To Reverse a Gift Aid donation, please see here: Reversing a Gift Aid
Once fully reversed, either delete/cancel the incorrect Gift Aid Declaration from the Constituent Timeline and perhaps an Activity note to the timeline to explain this for potential audit purposes.
Then navigate to the correct Constituent Profile and add a Gift Aid Declaration to the Timeline
as described here: Adding a Gift Aid Declaration