Is it permissible to pay off a mother’s debt from her entitlements without the heirs’ permission, and is it necessary to inform them of this, especially if informing them might cause problems?

If the question is about a sum of money your mother received after your marriage, and the Pensions Department is demanding it back, then this is a debt owed by her that must be repaid before her estate is divided. Its repayment does not require permission from the heirs. If informing them would lead to problems, then do not inform them and repay the debt, because the deceased is held by their debt.