My thoughts are to leave it in place and work around it. I think any attempts to remove it will result in its destruction. The only other option I could envision is to take a very good photo of it and have it reproduced.
After building grills for over half a century, I would have thought Weber would have switched to a more permanent/durable data plate. But, it seems like the newer ones are even worse. Try spraying any kind of cleaner on one and wipe it clean and you will likely be looking at a blank white sticker.