You might be suffering from chronic tonsillitis which can sometimes cause recurrent whitish debris collecting over one of the crypts of tonsils. Sometimes it can cause foul smell known as Halitosis. If there is a calcified hard stone over tonsil it can be removed but soft debris can't be just managed by removal, you may need to undergo surgery known as tonsillectomy
Next Steps
Consult nearby ENT specialist for confirmation of diagnosis and appropriate treatment if required