Yes, plug the holes from the back as mentioned above. Let the metal cool before doing the next one since the holes are close together.

I like to grind welds close to flush with an abrasive sanding disc (sandpaper "flapper wheel" or whatever they are called) rather than a rigid grinding disc and then carefully hand file the last bit to match the adjacent metal. Takes longer, but worth it.

If you do it right you should be able to get it fixed with nothing more than a few coats of primer and some blocking to get it flattened out.