Can you share a photo? I’m not sure what open presses are. :)
Not sure what you mean by open presses? Like a wine press?
What is your goal in putting something behind your presses?
Are you referring to your cupboard door open/close presses?
Can you repost the question with more information or other wording? Sometimes a photo helps.
Having a visual might be helpful to be able to offer the best guidance .....to a help find the best suggestions or potential solution for your problem.
An open press is an Irish airing cupboard, usually with slatted shelves. Sometimes, the controls for the hot water tank are located inside or behind the same area.
Catherine's posting of her kitchen open press would be of help to those in the U.S., for better assistance on her situation.
Perhaps a pretty fabric stapled or glued to the inside of the frame?