you can't except by closing & restarting GMS2 to remove that buffer (if by get rid you meant the little button thing that appears under the default 10 round & square brushes which contain the last five copy/past that you can use as brush if you want or not )
it is unusual, but I don't find it that bad; seriously I would like to see more drawing app offering a buffer of the last 5 cut/copy
It's is pretty bad actually. try pasting a 1028x1028 image on a sprite of the same size when you dont have the entire canvas showing. it becomes a brush with the mouse at center of the image. try to position that image in a pixel perfect manner... You have to zoom out and scroll the canvas to the point it is entirely visible and click hoping you are right on. then zoom back in and realise you misaligned it...
The paste should drop the image on the canvas and enable that rectangle select mode, which in turns allows me to decide where from the rectangle I want to start dragging at any zoom level and any canvas scroll position.
It you want to paste a brush, right click the brushes and select paste from the (non existent) right click menu