You're asking for help with a folder filled with stuff you don't want where it's located. That folder happens to be the Desktop, but it could be any other folder under your home folder.
Some errant sequence has filled a folder with files that you now don't want where they are located.
Only you can decide what's in those files, whether to preserve those files and where you want to copy those files, or whether you can or should delete those files, or a combination of both. If you want to keep those errant files, create another folder under your home folder or your documents folder, or however you organize your files under your home directory. Copy the errant files there with an individual drag, or a mass-select drag.
If they're screen shots or other images, preview them—Quicklook or otherwise—and see if you want them.
If you had previous files in the desktop, then you'll have to sort those out, if you want to keep those files on the desktop—in the desktop folder.
If the screen shots all happened around the same time, selecting a different sort at the top of a Finder window might make it easier to mass-select the errant files.
And again, ⇧click and ⌘click and ^click are useful for selecting and de-selecting individual files and ranges of files. This for dragging some or all of the files in the source window in Finder.
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