One could pretty much map the distortion with a rectangular grid with no extra test equipment.
There's four individually positionable traces, which with their inputs grounded should be horizontal lines, so you could set up the four traces at 1 div vertical intervals on the lower part of the screen, against the undistorted right edge to check the distortion. There's also a delay timebase with a trace separation control , so in at least one of the delay modes in the right delay mode, you coudl use the trace separation control to put four more traces on the top half of the screen, or to get more lines on the bottom half, for a total of eight horizontal lines. If you cant figure that out,
simply take another photo with the traces set up as horizontal lines on the top half.
Similarly for vertical lines, use the calibration signal on a single channel, adjusted to just go off the screen at the top and bottom, and adjust the variable timebase and x position to get a line on each division checked along the undistorted top edge.
Overlay the two photos and you've got a good map of the distortion.