Remove other cars paint from bumper

I don't know if I have the authourity to answer this. But, I am a auto refinisher of 8 years now and I know this situation. First, I would try just a bit of paint thinner on a soft rag, most times that'll whip it right off with out softening your paint.
If that doesn't work, try some rubbing compound with a soft rag. I like 3M part #06060. Most auto stores have it and it's usually around $15.
It takes a little elbow grease, but it works. If it's that deep and still won't come out, you may need to see if any of the body shops around your town will buff it with an electric buffer real quick. Hope that helps

Thats awesome bud. Thank u so much. Much appreciated. :D

Some people said if I wet sand it a bit that will work too. Any opinions?

You could, but you're in danger of going through the surrounding clear coat you don't want to take off. Personaly, I would try the thinner first, and if that doesn't work, then maybe try some 1500 or 2000 grit wet/dry sandpaper and take it slow, then buff it out with the compound I mentioned before.
That should take anything off.

Ah ok. Thanks alot for the help bud! Definatly made my day better! I will take a before and after pic if I can post it on here.

Thanks again!

Well I finally just got to trying the paint thinner idea for removing the smudge of paint on my car. And it worked wonders! Looks like brand new again. Just wiped it down with a damp cloth after to remove any paint thinner so it doesnt soften the paint anymore.

Thanks alot for the advice!