Worst case scenario would be epoxy.

Try using a drill bit of the right diameter and tapping it sharply with the side (cheek) of a hammer and be sure to wear safety glasses to do it! Only the "bell" (face) of the common hammer's "Hammerin' Parts" is hardened and a drill bit is definitely hardened and you NEVER strike hardened steel with hardened steel. That's what Ball-Peen, Chisel and Lump Hammers are for, hitting hardened chisels and punches.

You're not likely to bend a drill bit, the point isn't going to go through or dent the logo unless you're banging on it way too hard and by then, the bit will have shattered at that diameter. Drill bits are pretty inexpensive at that size and it's handy to have several of them, cuz you're likely gonna need a new one and it's tough to find 'em in onesies!

If it's epoxy and hasn't come off by this method, you'll probably need to grind off the backside to get it loose and then build it back up again with something like epoxy putty or Bondo to re-install it . . . or that's how I'd do it if I only had simple tools . . .

. . . if you've got a flat punch that small you're in business . . . or file a nail flat . . .

. . . but that'll be shorter and . . . YOWCH! )