Is it permissible to return to a wife divorced through a "divorce for release" (طلاق إبراء), with whom a marriage contract was performed in a hotel without a guardian or witnesses, and with only the knowledge of the hotel staff?

If the divorce mentioned is Khul', then it is an irrevocable divorce (baynunah sughra). For the wife to return, a new contract and a new dower are required, and the contract must meet all the conditions for a valid marriage. Any marriage conducted otherwise is considered void. Repentance to Allah is obligatory, and the contract must be renewed in the presence of the guardian and witnesses. If the family refuses, they can be persuaded, and their refusal does not invalidate the contract. If the guardian withholds consent, the woman can refer her case to a judge to marry her off. However, if it was not a Khul' divorce, and it was the first or second divorce, the woman is still under your marital authority, and she can be taken back without a new contract. The family's consent is not a condition, based on the Almighty's saying: "And their husbands have more right to take them back in that [period] if they wish reconciliation."