If it's double-sided foam you should be able to stick a sewing needle or pin in quite far. If there's no screws on the back what else could they use. If you pry on it I would protect the surrounding finish. I have used one flat or flat ended pry bar to protect the finish while prying with another one. You also need to think about how you are going to attach the new pull/handle. I might suggest mineral spirits or lighter fluid to remove the old adhesive. I don't recommend Goof Off as it contains lacquer thinner and will dull or remove most varnish. Good luck.
An Old Fisherman
2017 Nexus Ghost 36DS, 2014 Ford F150 Long Bed
2007 Harley-Davidson Ultra Classic