What can I scrub paint with?

I have a stubborn something on my hood (no idea what it is), and am wondering what's safe to scrub it with. I think I need something on the abrasive side, but of course don't want to mess up the paint.

It looks like ketchup in color, but it's been there for several months and through several washings. I can kind of scrape it off with a fingernail, but there are a bunch of spots so that'd be a major pain.

I got after it with a rag yesterday, and one or two spots came off while others just stuck. What can I use? Maybe a green dish scrubbie from the grocery store?

Thank you.

 

Clay bar. Keep in mind though if you have a dark colored truck that you will have to follow up with a good polish and then a good coat of wax or sealant. The method I use is wash, clay bar, Meguiar's Ultimate Compound and then Meguiar's NXT Tech Wax.

 

3m polishing compound works good on paint scuffs and light stuff, wont scratch your paint either.

 

Thank you. I never had a vehicle I cared about before, so didn't know where to start.

The clay bar sounds like a little more work so maybe I'll start with the polish and see if that gets the gunk off. Then go to the clay bar if necessary.

 

Actually clay is not hard at all.