Barbara this is a tough one. Is it plexiglass?
I hope you find a solution. I’ll be following this one.
Depending how deep they are & if glass is coated polishing compounds, maybe toothpaste https://www.youtube.com/watch?v=JErQ72NH4jA MORE https://www.youtube.com/watch?v=k1B_puVXtxk
Apply a drop of polishing compound to the buffing pad. Polishing compound is a fine powder used by jewelers and glass craftsmen for polishing gemstones and glass. It can be found at craft stores, glass retailers and home improvement stores.
Buff the compound into the scratch using a gentle, circular motion. As you buff, check in on the progress of the scratch by wiping the compound away using a clean cloth. Continue buffing until the scratch has disappeared.
Soak the sponge in rubbing alcohol then wipe the surface of the glass. Clean all traces of polishing compound from the glass.
Dry the glass using a lint-free cloth. The scratches should be less noticeable and faint. If they are still deeply embedded, contact a glass professional for replacement or professional scratch removal.
A dog wouldn't be able to scratch real glass unless there is some kind of coating on it that the nails would be able to scratch. I would check to be sure they aren't plexiglass or have a coating of some kind on it.