Push on the "plug" with something like a phillips screwdriver, etc while pulling up on the faucet handle and it will come off. No set screws are involved.
After you get the handle off go ahead and remove the entire faucet from the vanity and get one from Lowes, Home Depot, etc to replace it because it is JUNK. I replaced ours with a single handled Moen and it works great (and QUIET). Dispose of original faucet any way you prefer.
