In my Oxford Unabridged Dictionary under "Pressing -Iron" there is reference to a literary entry of 1658: ..".take a Taylor's iron made hot and rub it up and down upon the cloth" There are earlier references too. Therefore...."refrain your suit from pressing" had more than 200 year of precedence in possibly humorous meaning. It is always dangerous to underestimate W.S. Gilbert.....one of the funniest and most brilliant librettists of all time. This entry is response to britty280292.
If her garment is a pinafore, W.S. Gilbert is perpetrating double on the audience..a pinafore on the Pinafore, so to speak. There was nothing of which he was not capable......greatest English poet with Kipling and Burns......and his father was a naval surgeon, so he had inside knowledge about the navy. In "refrain audacious tar your suit from pressing" is he referring to the care of a garment??
The word 'suit' is an abbreviation of 'pursuit'. That is, do not continue your pursuit of your goal. Shakespeare uses this in wordplay in "As You Like It" when Jaques says that he is 'ambitious for a motley coat'. His king 'You shall have it', to which Jaques replies "It is my only 'suit", in the double meaning of 'it is my only pursuit' or 'it is my only request of you' as well as 'it is my only set of clothing'.
I am aware of the meaning of the expression..but I wonder if W.S.Gilbert was using it in 2 meanings Only knowledge of the care of garments at that time can answer that question. When did pressing of garments start? I will have to investigate.