TL;DR - given a sample of bone which has been encased in asphalt for tens of thousands of years and has become saturated with the asphalt, how can you get an accurate age for the specimen through carbon dating?
This past weekend I took my kids to the Page Museum at the La Brea Tar Pits in Los Angeles. While there we saw an astonishing number of fossilized Pleistocene animals. The interesting thing is that all of these fossils have a lovely (to my eyes, at least) brown color which is staining from the asphalt in which these bones have lain for thousands of years.
While there, we saw a presentation which explained that the asphalt seeps into the porous bones and it was explained that we know how old the specimens are through carbon dating. Which got me thinking - if the specimens are all highly contaminated with asphalt, how can they know that the sample they're testing contains carbon from the bone and not from the asphalt (which is presumably much older than the bone)? I did try asking one of the docents, but they're really not equipped to handle such a technical question.