Compound, something like a 1000-1500 grit. should be able to get it off just by rubbing, if not, get the shop thats painting the spoiler to buff it. Clay bars just remove any dirt or deposits in the paint, the wont remove stains.
I used to use a product by 3M called Finesse-It which is like a mild rubbing compound. They used to sell it at automotive paint stores. Works well for removing nasty bugs, tar, sap, rubber, etc. but also removes any wax in the area. But as mentioned you might need a regular rubbing compound.