How do I get cooked on grease off of my black stovetop?

You can try making a paste with baking soda and white vinegar,applying and leaving on long enough to break down the grease.

I have a glass top and clean the really thick stuff with a razor blade scraper. Be careful to hold it at the right angle so not to scratch. The cleanup with what's left or not so yucky areas is best accomplished with Bar Keepers Friend- the powdered kind. Mildly abrasive and it has become my best friend!

Glass window scraper! Keep stove top wet to avoid scratching. Follow ups with a mild powdered cleaner.

please do not use a razor or scraper. leave whatever solution you decide on the stove and use Mr clean magic eraser instead.

Bar keepers friend will help loosen it as well!

Since this is a rental I'd ask the owner for help. Plain water and a wet cloth will do a lot but eventually you may have to resort to stronger methods and that's why I'd ask her or him.

Stubborn grease on the stove top and control panel -- straight ammonia. It works like a charm. You don't need much, just put it on a sponge or paper towel.

Try 'Awesome' it's a cleaner sold in DollarTree Stores it is strong. Spray the grease leave on for an hour or longer the solution will soften the grease for easy removal, it only cost a dollar and the refill bottle is larger & cost a dollar too! Awesome cleans alot surfaces sometimes you may have to dilute with water but most times works great straight out of the bottle.

I don't know what will work best - plenty ideas above. I do know that I would talk to the landlord to gain permission to try a few of the ideas, that way if something goes wrong you have had appropriate permission. It should also put you on good terms with the landlord as it proves you care about the place that you live in. I would avoid scrapers.

I use a razor blade and simply cut it off. Must be glasstop!!! Turn blade to a 90 degree angle.

First, I am amazed the landlord did not give you a clean house, especially the stove. Makes me wonder about maintenance on the rest of the house. That being said, I also have a black stove / appliances. I would soak with hydrogen peroxide, rinse then the vinegar and baking soda. I wipe my stove down every time I cook, and I cook every day as I make my own pet food. Hope your rent is cheap. Good luck!