You have absolutely no lawsuit in this case
You have already been made whole, they took the burger off your bill, so you are not out 1 penny. I am guessing you will get a couple gift cards for maybe $25.00, but no money from the company, and they will of course send you the routine "we are sorry" note and that is it.
You were not injured, you did not seek medical attention and in fact I am betting you do not even have the object you claim was in the burger and even if you did, so what you were not injured.
The company removed the cost of the burger from your bill, that is the only compensation you will get, anything else is a bonus