Where you at with this?
That almost looks like some kind of pattern left by a paint roller? Does it look like some type of paint?
Here's your options,
Clay - Get an aggressive clay and rub hard and fast with lots of lube.
Nanoskin towel - Get a medium grade and rub hard and fast with lots of lube.
Aggressive Compound - I'd probably use
Pinnacle XMT #4 as it's more like liquid sandpaper. One of the hi-tech compounds like M105, etc. use abrasives so fine these types of products feel like hand lotion. You want something where you can feel the grit in the product.
Wetsanding - Probably have to use #1500 to #2000 - Be very careful if you take this approach.
Dissolve by solvent - Lacquer Thinner, Goo Gone, Goof-off, Mineral Spirits, Xenit
All of the above will either mar, scratch and dull the paint where you work so after you've removed the offending substance you will then need to polish the paint.
If you're new to car detailing, maybe start a thread on this forum with a title like this,
Pro Detailer wanted in Resume Speed, Iowa
We have lots of talented detailers on this forum and there's probably someone near you that can help out.
:dunno: