Delete attachments below min file size?

Clients send emails with their social icons, banners, sigs etc at the bottom but these are attached to the ticket and use up the file limit. I’ve increased the number of attachments allowed per ticket but it still creates a mess and is difficult to identify a real attachment.

Is there anyway to only attach files over a certain size or delete below that limit? Say 1000 bytes? This will filter out the Facebook, Twitter and other fluff.