Can I warp this vintage illustration into a proper rectangle?

[Ofnuts]

You use the Perpective tool in "Corrective" mode: You start the tool, set it to "Corrective mode" (this can be made a default), drag the four corners to points that should make a rectangle (I used the corners of the black frame) and hit "Transform".

But:

• The contents of the shape in the perspective tool is mapped to the canvas, so part of the image are outside the current canvas, to get the full image you have to use Image>Fit canvas ti layers
  
  
     
  
  
  
• But this also often stretches the image in one direction, so you have to use the Scale tool to scale the image in the appropriate direction to restore the aspect ratio.