Sorry to hear that!

I wouldn't worry about eyes on your card for this kind of thing. Your options are to do nothing so you don't lose your ST DL options... but that is not an option here. Or to call them and get it fixed ASAP!. You will likely be talking to a department that is NOT the same people as the ones who you would be worried about. getting a new card due to loss is a standard practice and they will just verify with you that it was in fact you who made the last transaction(s) etc and that is that.

Now here's the good news that may still be true: It is possible (surely not always the case, so YMMV) that their issuing you a replacement card might give you a new 5k sign up miles! Even though your account is not new. I have seen it before (I had 2 accounts and both cards got compromised but were still in my possession) and it happened for me. They charged the fee too but I called in to have them waived later. They never took back the miles. So, it may work for you but don't count on it lol

Good luck.