TimeMachine gives me pixelated screen on my iMac

Hello Loran Kary and welcome to Apple Support Communities.

You appear to be having an issue involving a backup drive.

Your best option will be to start by isolating this to either the drive or software.

1) Start by doing a safe boot of the Mac. This will clear some cache files, turn off some system extensions and log-in items and give you a good foundation. After doing the safe boot, reboot normally and test.

How to use safe mode on your Mac

2) If the issue persists after a safe boot, set up a test user account in order to isolate the issue to the system or the user data and ultimately resolve it. 

How to test an issue in another user account on your Mac - Apple Support

If the issue is present in a fresh test user account, then the issue would appear to be isolated to the drive you're using. If it does not, then this may be related to user data.

Cheers.

Hi Loran Kary.

Very glad to hear that booting to safe mode seems to have resolved the issue.

In terms of what safe mode actually does, to quote the official Apple resource:

"Safe mode prevents your Mac from loading certain software as it starts up, including login items, system extensions not required by macOS, and fonts not installed by macOS. It also does a basic check of your startup disk, similar to using First Aid in Disk Utility. And it deletes some system caches, including font caches and the kernel cache, which are automatically created again as needed."

How to use safe mode on your Mac - Apple Support

Have a super groovy rest of your day.

Cheers.