How to get rid of little floating windows in iOS15

I suspect that you make reference to the “Shelf” - this being a new feature of the now revised iPadOS multitasking environment. 

iPadOS permits you to have multiple “instances” of the same App - each instance being self contained. The shelf, when triggered, shows a thumbnail of each running instance of an App. 

For example, if you have three running instances of Safari, each with its own set of open tabs, you will see three thumbnails corresponding to each running instance of Safari - plus a button to open a new instance of Safari. Simply tapping a thumbnail will switch directly to that running instance of Safari. Each App has its own corresponding shelf.

Individual open instances of an App can be closed directly from the Shelf; just swipe the unwanted thumbnail off the top of the screen. Note however, that Multitasking and associated Shelf functions cannot be disabled.

This article from Appleinsider has a useful explanation of this new feature along with many of the updates to multitasking:

https://appleinsider.com/articles/21/08/12/how-to-master-multitasking-on-ipad-and-ipad-pro-in-ipados-15

The iPad User Guide is also a rich source of frequently overlooked information. 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

Only one person can be “first” with correct analysis of your issue. As for fulfilling your your wish, that is considerably more difficult; neither multitasking, nor individual elements of it (such as the App Shelf feature), can be disabled in iPadOS15.

Whilst respecting your viewpoint, I can only recommend that you stick with it. Besides having few alternatives, there is rationale to this suggestion…

Multitasking in iPadOS15 has taken a substantial step-forwards. The fledgling multitasking environment of iPadOS13/14 was difficult to access and functionally manage - the previous limitations have now been transformed into functions that are now easy to use. To achieve this many aspects of the User Interface (UI) controls have been heavily revised or are new; the shelf is one of the new features that, for many, feels very alien to the aesthetics and control logic to which you have become unconsciously accustomed.

As a consequence, some “adjustment” will be needed before the new reality will become second nature. Speaking personally, having worked heavily with iPad and iPadOS over many years, I believe that given a little time and perseverance you may eventually discover the benefits of the revised iPadOS15 UI.

In the meantime, Apple invite submission of constructive comment and feature requests via their Product Feedback pages. If you have suggestions for how the UI might be improved, this is perhaps the most appropriate channel to make your views known to Apple:

Product Feedback - Apple

AKRBTN wrote:

One tap somewhere else on the screen and they’re gone.

As fully described in the linked web pages.

One tap somewhere else on the screen and they’re gone.