If a noncustodial parent gives up his/her visitation rights. can they take the parent back to court?

i was asked to give up child support and back support and the noncustodial is willing to relinquish their visitation rights. is it possible for the noncustodial to take me back to court to get their visitation reestablished? Let me add this, the children involved didn't see this person for four years and the person was granted limited visitation and later counseling. Now, this person wants to give up visitation even though the children wants to be adopted by their step parent. Children are teenagers.