Is it permissible to refuse an offer from a female relative to cover the expenses of Hajj due to her reminding of her favor and her harm, given the existence of debts that currently prevent performing Hajj, and the desire to perform Hajj later after settling these debts?

The questioner's brother is not obligated to perform Hajj by accepting that relative's offer, especially if he is boastful about his gift. This is because accepting a gift from this type of person causes severe distress to the recipient, and Allah does not burden a soul beyond its capacity.