So no to removing then? Will the corydoras be okay?The glass shelves are bracer bars to stop the glass bowing outwards under the pressure of water. Some tanks use these, others use a strip of metal or plastic running from front to back over the middle of the tank.
I used to have a Juwel Rio 125 which has a plastic bracer bar attached to the top trim at the front and back of the tank. I noticed that a gap was developing between the lid and the trim front and back in the middle of the tank and when I investigated I discovered that the bracer bar and attached trim had pulled away from the glass and the long sides of the tank were bowing outwards.
Not being confident of my DIY skills, I replaced it with a custom built tank which has the glass shelf bracer bars, and these double up as supports for glass sliding covers. You could use them to hold a condensation tray if one will fit under the lid.