I want to remove the Adopt button from the Document Overview part in the ME21N screen. But the button is not contained in the GuiXT screen elements.

This is a special toolbar control that cannot be changed by GuiXT.
What you can do is to suppress the function behind the button and to display a message instead:

On control="Toolbar" item="COPY" event="1" process="no_adopt.txt"

with the InputScript "no_adopt.txt":

Return "E: Please do not use function 'Adopt'"  -statusline

You need the "InputAssistant" component for this approach.