It is not permissible to swallow it intentionally. You could have spitted it out wither on the carpet or put it in your clothes rather than swallow it.

And Allah knows best

I had something stuck in my teeth during the fajr prayer. I swallowed it. Although, it was an accident when I swallowed, it was only partially an accident,had I fished it out I would have intentionally swallowed it since there would be no where to spit it out besides the carpet or in my clothing, did this invalidate my fast that day?