See you in the funny paper[s] means "Goodbye, see you soon".
A Dictionary of Catch Phrases (1986) by Eric Partridge and Paul Beale says:
see you in the funny papers (—often and orig. I'll). 'This jocular farewell suggests that the person addressed is rather laughable: US: 1920s; extinct by the 1950s' (R.C., 1978). Perhaps adopted in the UK from American servicemen c. 1943. By c. 1955, (I'll) see you in the funnies.
The OED has funny paper from 1874 and funny column from 1860, meaning "a (section of a) newspaper containing humorous matter or illustrations".
The earliest example I found of the phrase is in a letter in Commercial Telegraphers' Journal (August 1920, Vol. XVIII, No. 8):
So long, boys, see you in the funny paper. "30."
J. N. HANNA,
Another in the Union Postal Clerk (March 1921, Vol. XCII, No. 3):
We will see you in the "funny paper" next month.
Here's a April 15, 1921 letter published in University of Virginia student paper The Virginia Reel (April 18, 1921 Vol. 1, No. 8):
Well, boys, must close now. La, la, till the next time, and I'll see you in the funny papers. Ever your, ADELAIDE.
Here's a 1922 example in the signoff of a report in The Tusla Scout from Troop 12 by Ed M'Lain (published in The Tulsa Daily World, March 19, 1922):
Good-bye, see you in the funny paper.
This use by scouts suggests it's not insulting, but may be used in a good-natured, light-hearted mocking manner.