I had sticky glue residue of masking tape on window and body of car due to a window replacement. Thinners for the window and then my sister surprised me by saying to use Doom (mosquito spray) . Worked like a charm .. had to soak it for about a minute ... it is also used to remove tar from body of a car.
You can buy both attachable backrest and headrest.
If that is too pricey pick a tall broken chair on ebay or from garbage and fasten backrest from there to you chair with belts. If it comes with headrest then you are lucky if not then make sure to get a backrest which is easier to mod.
If the whole construction is too ugly, you can also buy a stretchable ...
If you can place something around the desk (top, behind, underneath and front to connect on the top again) you can then 'lock' the chair underneath the desk to that item.
I would go for a rope and a good knot the kid can not yet untie, but most people will go for the ratchet straps. It you run two side by site and knot them together in two places you make an ...
Assuming that plywood covers the back of two long sides, but none covers the two short ends:
Position the desk so that one of the short ends touches a wall.
When you finish working at the desk, pull it away from the wall.
Position the chair against the wall as though you are going to sit at one end.
Push the desk back to the wall to trap the chair.
If your child has trouble moving the chair and it is in an inconvenient location to use for climbing, this idea may work.
Place the chair wheels/casters into cups (jar lids) so that the chair is difficult to roll around. You'll have to pull it into position; but, it shouldn't be too difficult for an adult.
When the chair is unoccupied, remember to slide it ...