I mean, I have never had a metal card so I can't say with any certainty but I would bring it to Chase. I doubt they would just throw it out, as that is more of a risk on their end at that point, and I would guess they probably recycle them (whether it be the metal or maybe the chip). If they don't recycle them, I would assume they at least shred them or dispose of them properly. You can just go to the branch and ask them if they take back old cards and what they do with them, worst comes to worst they say no or don't dispose of it in a good way and you deal with it in a different way.
We're trying to dispose of the card NOT the microwave here old man jeez.
Another vote for the Dremel. I used it to sand away 1/8" of metal from a stainless steel bracket, so it should have no issue grinding away the engraved numbers.
I'm sitting here pondering my old childhood hobby that somehow didn't get me killed. I crossed railroad tracks to/from school as a kid. If I timed things just right, I could hear the freight train on the way as I was nearing the crossing.
They really do a number on pennies.
I wonder about metal cards.