Is it permissible to pay money to employees in the control room to raise my daughter's grades, given that she was wronged in the exam results, and knowing that this action will enable her to join the college she desires, and is this considered unlawful?

It is permissible for someone who feels wronged by exam grades to appeal for a re-evaluation of their papers. If the appeal is unsuccessful, and it is confirmed that deserved grades were not counted, or a paper was switched, or there was an error in summing grades, and the right can only be obtained by paying money to the one who takes it, then it is permissible to pay this money, while it remains forbidden for the bribe-taker to accept it.

However, if the decrease in grade is due to the grader's assessment of the answer, then paying money to increase the grade is considered forbidden falsification and cheating, which is one of the major sins.

Since ascertaining deserved grades that were not counted is difficult and rare, one should be content with Allah's decree and ask Him for goodness and blessings.