quickly remove screenshots from desktop

Yes. Open a new Finder window and click on the Desktop in its sidebar. Then do a ⌘+F to start a search with this criteria: Name contains screenshot. You'll get this (I have only one screenshot on the Desktop):

Then you can do a ⌘+A (select all) and drag them to the Trash bin.

On your Desktop, right-click and choose Use stacks from the secondary menu. Your screen shots will all be collected into a stack named Screen Shots. Click on that stack to open it, select the first screen shot, and press the space bar to display that image in a Quick Look Window. If you want to delete an image, then press cmd+backspace to move it to the Trash, and the next image will appear in Quick Look. If you want to skip over an image to save it, use the down-arrow key. Don't forget that if you accidentally delete one of these you want to keep, open the Trash folder, right-click on the redeemable image, and choose Put back.

Right-click on your Desktop and click that Use stacks menu item to disable that feature.

Empty the Trash when you are finally done.

Command-click on the ones you want to delete, then click on one and drag them to the Trash.

Probably you should first find the ones you want to keep, and move those to a separate folder-- and maybe put that folder in your "Pictures" folder so you don't accidentally delete them.

Or… Select them all , command click on the ones you want to keep which will de-select them, drag the rest to the Trash.

You are welcome.