Does the prayer of one who repeated the Basmalah twice in Al-Fatihah during the fourth rak'ah of the 'Asr prayer, and did not perform the prostration of forgetfulness, become invalidated?

Repeating the Basmalah during Al-Fatihah is considered an additional utterance. Prostrating in forgetfulness (sujud sahwi) for it, if it was done out of forgetfulness, is a matter of scholarly disagreement. However, not performing the prostration does not invalidate the prayer. Removing something from the mouth during prayer for fear of swallowing it is a minor action that does not invalidate the prayer.