I see these tiny colorful pixels on my screen which (seemingly) do not go away.
The reason is probably me wiping off smudge with paper or whatever I had around the house.
Is there a way to get them off? I don't want to try "scrubbing" any harder.
There are two possibilities: dirt on the screen, and actual internal dead pixels.
If it's dirt on the screen, then since it doesn't sound like you've tried this already, I suggest water. Water will not hurt your screen, as long as it does not run down into a crevice and into the electronics. Use a damp microfiber cloth if you have one; otherwise, use a damp paper towel very lightly (paper towels can be scratchy). Most crud that you can get on a screen will wipe away easily with wet wiping; you do not need to scrub hard, and you shouldn't as this could scratch the screen or damage the internals.
When I say “damp”, I mean getting the cloth wet under a faucet and then firmly wringing it out until it doesn't drip. Dry water off your hands so they don't drip either.
On the other hand, a colorful single pixel defect may well be a “dead” pixel. (Dirt on the screen typically doesn't look colorful except when it's fresh liquid droplets, which act as little lenses magnifying the pixels.) Typically, there is nothing you can do about these, but I have seen occasional reports of a dead pixel being restored by gentle rubbing. I would not recommend attempting this, myself.
If the pixel is always there, i.e. "on", it is a stuck pixel. Apple's quality control allows a number of these per square inch.
So if your Apple is new (or in the warranty period) and it has a couple of these you will not get an exchange for a new computer.
If it is out of warranty, you can try to "massage" the pixel while the computer is off and, keeping pressure on the pixel while booting up, stop the massage when completely booted up.
There are websites (mydeadpixel.com) and programs you can try that flash bright images. These sometimes cure the problem, but only rarely.
Google Fix-a-Stuck-Pixel-on-an-LCD-Monitor and you'll find a few more things to try...