Not to mention that every single person given such a business card, client or not, now knows where to go find that person if they are no longer employed by you. I doubt this is something you want to facilitate, and the advantage is 100% to the MLO in this request. In my opinion this shows that the MLO doesn't particularly view themselves as being your employee, but rather an entrepreneur who just happens to work out of your space. In my experience this can sometimes mean that this person is not always working to your institution's advantage.
"You win some, you lose some, you wreck some." -- Dale Earnhardt