I would thread in a loop of wire at each corner (or near to) and use that to pull up. Usually the grill is crimped to make it wedge into a groove. (OK that is how mine all came out - several other brands of speaker)
Good - Fast - Cheap: Pick any two.
E23 735i; E32 735iL (X 2 - 1 Alpine White and 1 Glacier Blue); E34 535i; E38 735iL; R50 Cooper; R55 Cooper Clubman.
E21 318i; E30 318i; E32 735iL; E34 535i; E38 730iL; E53 4.4i