Not the caliper but the part in moves on
http://www.realoem.com/bmw/showparts...95&hg=34&fg=10
#8
Disassemble, clean and lube. Also wire brush the areas where the caliper rides in the bracket.
If the caliper itself(piston) were stuck the brake would always be dragging or not apply at all.
PS Garage couldn't check it?? Monkeys, find a new garage or do it yourself.