Should you write a thank you letter after an interview for a part time job for a grocery store for example?

It isn't necassary, but it won't hurt your chances of getting hired. And it shouldn't be written as a thank you note. It is a follow up letter. You may thank them for the interview, but mostly it should be about looking forward for the oportunity to work there. Don't sound like you already have the job, but like you are hopefull that you will get it. yes