After having performed Salaat I realized that a particle of food was stuck between my teeth.

Answer

Rinsing the mouth during wudhu is Sunnat. It is not Fardh. Therefore, even if someone forgets to rinse the mouth, wudhu will be valid. The particle of food in your teeth did not affect your wudhu. Your wudhu was valid and would have remained valid even if you had not rinsed your mouth again. However, if ghusl is Waajib, then it is Fardh to rinse the mouth. In that case too it would have been necessary to only rinse the mouth again, not make the whole ghusl from the beginning.