Should read whatever contract you sign. There's almost certainly a provision for how your blood is handled. It's mostly to keep people from thinking that the place might give your blood to someone and put it in a database or whatnot, -but- it also serves as them letting you know you aren't getting it back.

Edit: Just remembered some places do infact keep your bits after testing, but that's for like when you provide your blood to a research project, not like STD tests or whatnot.