You searched for: “waive
waive, wave, wave
waive (WAYV) (verb)
1. To refrain from insisting on or using a right or a claim: "Ed will waive all rights to the money he has inherited so his daughter can have enough funding for her university expenses."
2. To abstain from applying or enforcing a rule, a restriction, or a fee: "The college will waive Mary's tuition expenses because she has a scholarship that will pay for the necessary costs."

"The schools waive the costs for books for low-income students."

wave (WAYV) (noun)
1. An area of moving water that is raised above the main surface of an ocean, a lake, etc.: "There was a huge wave that almost upset the boat."
2. A strong feeling that suddenly affects someone: "An unexpected wave of fatigue overcame Robin after working two days without sleep."
wave (WAYV) (verb)
To make a repeated movement of the hand or of something held in the hand; especially, as a signal or greeting: "Frank saw Jill wave her hand hello after the train came to a stop in the station."

With the wave of her pen, the librarian was able to waive the overdue fine on the book which Frank lost and he was happy to wave goodbye as a sign of appreciation.