My whole career was in the consumer products industry. So I need to ask if this was in actuality an antiperspirant stick (containing aluminum and zirconium and stearyl alcohol) as opposed to a deodorant-only stick. If deodorant-only stick melted, soap and warm water should work, "wet" the whole seat not just the spot.
If antiperspirant stick, hot water and soap will help some to dissolve the aluminum-zirconium-glycine-chloride complex, maybe try some denatured alcohol to remove the organic matter after that. Stronger solvents like acetone, dimethylformamide, or chloroform m and complain, maybe theyay dissolve the seat material as well as dissolving the antiperspirant.
Maybe call 800 customer service hot line of company that made it (I no longer have any stock of any kind) and complain, send your photos. The company I worked for oftentimes honored such claims.