Well apparently you are out of luck.
You could try to ask for a replacement with a better/different model paying for the difference and returning the one you bought.
Alternatively if you are really bothered with that, and I feel you believe me, you could try to sell it on ebay for a lower price thanyou bought it making it clear that has a stuck pixel but also full warranty. That way you could buy another one loosing just some money in the process.

Which isn't to say that it'll work. It's a chance and a long shot at that. I've seen it happen (mainly with stuck pixels, never with dead ones - whereas both terms are still thrown together including advice on how to counter/fix them), but never after just days - took months or longer. And I'm not gonna try to talk you into keeping the thing if it really bothers you. As I said, sometimes it's enough to ask customer support (or the store you bought it from) if they can do something and if you're persistent, you might get your way. As it may be, I wish you the best of luck and I hope you can enjoy your monitor at some point. Replacement or not. :)

Other than trying to massage it, nothing else is likely to work. I fixed my dead pixel by massaging it but I have no idea if it would work in this case. Worth a try I guess.

I see you are from Germany. To your knowledge, the same law applies there too? It seems that the European "14 days" period, during which you can return a bought good, no matter the reason, extends only to online bought goods. If you go in person, inside a store, and buy a good, then it seems that store rules apply.

Yep, the returned monitors from US go to Europe, so you got one of those returns.

From Europe, I don't know where the monitors with 5 or more bad pixels go. Possibly Africa, where you have to have 50 or more bad pixels before you can return the monitor.

Anyway, I bought a HP 27w monitor two weeks ago. Luckily it didn't have any bad pixels. It cost only 149€ (normally 199€ here) as it was an opened (but unused) package. It is quite good for my needs.

https://www.amazon.com/HP-27w-Monitor-Black-Onyx/dp/B078D7D7ZY

Correct. You can't refund it within 14 days unless you ordered online/via phone. However here a lot of stores will not give you a refund, BUT usually you can exchange a product with another of similar price (paying the difference or taking store credit). I am not sure (I don't think that) this is a law regulation, but I've done that in stores over here.

Have you tried talking to the store?

Of course, I have! I tried to return it the very next day.

You could try a black marker.

I'm actually going to try that!

Got it.
Kind of dangerous to buy such stuff (TV, monitors) without testing, as you know.
When I was buying mine, I was ready just to turn 180 degrees and go away if seller wouldn't have tested the monitor I chose (didn't want to go that route you have to go now, sadly; especially because my monitor was one of the most expensive ones at that time).

Right, it wasn't clear to me (maybe I missed that piece of information), so I was just making sure.

As we get older, it gets harder to read the fine print. Scaling works perfectly sometimes, other times not so.

I have 1920x1080 on my 47 inch TV and no complaints here. :) My next TV will possibly be 65" 4K OLED something something, but then it is not like I will be watching or playing any 4K material on it either. My PC is not fast enough and I HD movies are fine to me.

I was thinking of buying a 27" monitor with higher resolution which would have cost around 500€, but I decided to go with this 149€ HD monitor of the same size. I figured it is so cheap I wouldn't regret it either way, and I didn't, in fact I was delighted how good the monitor is.

I didn't want a smaller monitor. I have two 22" monitors at my work and I felt that if I am going to buy a monitor at home, it will be bigger. 27" is fine.