You can definitely over clean. If the stamp is light in pressure or temperature (depth or color) you can easily wipe that out with too much moisture. On markings like that, you're much better off doing a lot of light passes rather than one thorough pass. However, if the glove is dry and stiff and you're able to soften it up, that may be an acceptable trade-off. All depends on what you're dealing with and what you want to gain from the effort.
Huntington Base Ball Co.