Does the prayer of one who salaamed out of forgetfulness and then performed the Takbirat al-Ihram become invalidated, knowing that it was not necessary for him?

If someone performs the tasleem forgetfully before completing their prayer, they must return to complete it if the interruption was not prolonged. Scholars have differed on the necessity of the opening takbeer (takbeerat al-ihram (definition)) upon returning: The Malikis consider it recommended, but the prayer is valid even if it's omitted. The majority view is to build upon what has passed without the need for an opening takbeer. The prayer is valid whether one says the opening takbeer or not, and there is no difference between one who intended to exit the prayer and one who did not.