I do not see an issue with not having a corporate logo on your access card nor do I see an issue with not having "a drop in any mailbox" message on them. The reason being that if someone loses their card, it will be impossible or very hard to find out for which building the card is used.
Also in the event someone wants to perform a targeted attack, forging a logo on a key card will be the easiest thing to do.
There are other points which are more important. For instance if someone loses a card, can you block it? Normally these cards just hold a token which is checked at the door against a list of authorized tokens. It is imperative that you can track all cards and block them immediately in case of theft or when someone loses them. So when a card goes missing you need to immediately remove the token from the authorized tokens list.
I think people thinking you aren't an employee if you only have the key card isn't necessarily a bad thing if you are supposed to have two forms of id on you (employee and key card).