Question Logo or Watermark on Bottom Right of Screen

The way I read this you're not covered by LG's burn-in warranty, because the monitor was used in a commercial environment.
https://hothardware.com/news/lg-issues-statement-on-oled-monitor-burn-in-warranty

Thankfully, LG's clarification, provided by its Head of Consumer PR for North America, is nice and clear to non-legal professionals. In a nutshell, as long as you have been using the LG OLED gaming monitor for "as intended (personal PC monitor) in a residential setting (does not support commercial usage like retail signage display) burn-in is covered."


Does your monitor have Screen Optimization and Pixel Refresh facilities, similar to this Samsung monitor?
https://www.samsung.com/us/support/troubleshoot/TSG10003240/

I'm still using an ancient 2006 Panasonic Viera Plasma TV and screen burn in from watching too much Eurosport has slowly faded over time and disappeared. You may just have to live with the annoying logo.

https://www.tomshardware.com/news/oled-burn-in-testing-10-months
 
OLED burn in.
That happens in oled monitors when a fixed image is displayed constantly.
Use a frequently changing desktop background and you may not notice it.
Use a screen saver.
Both can avoid added burn in issues.
The LG pixel refresher will do nothing about the burn in.
If the unit was sold "as is" you have little recourse.
If sold as new, return it for a new one.