How can I eliminate the three dots on my iPad screen that appeared after I updated to the latest IOS?

You can’t.

This is an integral feature of iPadOS 15 and the way splt screen and slide over screen multitasking are accomplished,,now.

If you do not ever touch these three dots, your iPad will never divide up its screen area.

If you do nit like this feature, then you can send Apple unacknowledged feedback about it here.

Tap the link below.

Feedback - iPad - Apple

The three dots “button” is a core element of the iPadOS15 User Interface - intended to simplify use of full/split/slide-over multitasking. This control cannot be hidden or suppressed - and neither can multi-tasking be disabled in iPadOS15.

Information about using multi-tasking (and by extension - avoiding it) can be found in this support page:

Use multitasking on your iPad - Apple Support

The iPad User Guide is also a rich source of information about using iPad and its many features. The Guide is available both online using a web browser (such as Safari), or as an Apple Books download:

iPad User Guide - Apple Support

https://books.apple.com/book/id1567104892

Apple do invite constructive feedback, comments and feature requests via their product feedback pages. For iPad and iPadOS:

Feedback - iPad - Apple