2 things: One is why was there grease in there, second is how to get it out.
New linings are needed, you will never, ever get the grease out of the old lining, lord knows Ive tried. Brake cleaner on the magnet, get it out of the little holes. But... You can get a complete backer plate assembly with shoes, magnet, and all hardware for for near the cost of just shoes... Thats how I go. Soak the inside of the drum with gas, a few changes are needed as the grease getr in the bolt holes. It may take a little time. New grease: I use mystic 3 hi temp as TS carries it and it is listed in my dexter axle manual.
Why was it there? Could be the owner never changed seals, used a low temp grease meant for bushings, or mixed greases. If the axle nut could not be spun off by hand it was too tight and overheated the bearings, melting the grease. Seals wont contain that. Also if it went without grease it may have overheated. Rust on the seal area, or the owner pulled the hub and re used a damaged seal. Nicks on the seal area can also cause this. Use a hand grease gun and spin the wheel while greasing once or twice a year on ez lube and it should be good. I still inspect and re pack every other year.