Tooth extraction


I got my molor pulled on monday and when it was done a few hours went by and noticed this white thing poking out and i thought they didn't get the whole tooth. I told my mom and she said the same thing happen to get yrs back and she got xray and it was just bone fragment from the tooth getting pulled. I googled it and it said the dentist can easily remove this with tweezers. My question is do i have to get it removed? Will the gum eventaully form over it or maybe fall on its on? Its kind of uncomfortable rubbing against my tongue.