You need to remove the plastic beading from around the edges of the glass. Sometimes the black rubbers need removing 1st before the beading will release. Use a paint scraper to remove these parts.
You can fit a white plastic pannel in place of the glass, your local glass shop/glazier should know where to get one from. They are usually quite easy to cut for a cat flap.
Once the glass is removed, measure the thickness, width and height to get a pannel of the same size.