David Craig sent in this photograph and asked "What does it really say and why doesn't it?":
The Chinese says xiánzhūshǒu 咸猪手 ("groper"), which is a noun derived from xiánzhū 咸猪 ("salted pork") + shǒu 手 ("hand") — adjective + adjective + noun. Thus, the literal meaning of xiánzhūshǒu 咸猪手 is "salted pig's knuckle / trotter" (cf. German Schweinshaxe; Stelze in Austria).
"Groper" is a derived meaning of the term xiánzhūshǒu 咸猪手 ("salted pig's knuckle / trotter"). As to how "salted pig's knuckle / trotter" acquired the extended meaning of "groper", there is considerable difference of opinion. I will give first the explanation that is most straightforward and is accepted by the majority of people, and then will go into some of the more arcane, recherché theories.
Before that, however, I'd like to mention that xiánzhūshǒu is the Mandarin pronunciation of what is really a Cantonese expression: haam4 zyu1 sau2 鹹猪手 ("salted pig's knuckle / trotter"). Note that xián 咸, which is the simplified version of xián 鹹 ("salty"), also stands for a completely different morpheme signifiying "all; whole; universal; general", which was the original meaning of the character before it was borrowed to stand for xián 鹹 ("salty") as well.
The connection between lechery and piggish behavior is not too hard to see, since there are a number of terms in Cantonese that attest to it (e.g., zyu1 gung1 猪公 ["lecher"]), and the association exists in many other societies as well:
In the sixteenth century the emblem books introduced a host of new symbolic animals into the company of the virtues. Thus Chastity riding an elephant fights with Lechery on the familiar pig in an engraving cited by Tervarent. (Helen F. North, "Temperance (Sōphrosynē) and the Canon of the Cardinal Virtues," Dictionary of the History of Ideas, Vol. 4, 1973, ed. by Philip P. Wiener)
Of course, the pig is most often linked to Gluttony, but Gluttony and Lechery (usually connected with the goat) are often related (e.g., Chaucer, "Parson's Tale", 836-8: "After Glotonye thanne comth Lecherie, for thise two synnes been so ny cosyns that ofte tyme they wol nat departe.") Claudine Fabre-Vassas, The Singular Beast states: "The pig is a creature divided. It incarnates the sins of lechery and gluttony…."
We have accounted for the connection between "pig" and "lechery", now what about the "salty" part? Many Cantonese have told me that it has to do with the term haam4 sap1 鹹濕 ("salty-moist", i.e., "lecherous"). I'm sure that will ring a lot of alarm bells here at Language Log, since there have been several recent posts on this forum about word aversion with regard to "moist"; perhaps the same feelings carry over into a completely different language.
An example of a directly relevant Cantonese term based on haam4 sap1 鹹濕 is haam4 sap1 lou2 鹹濕佬 ("lecher", lit., "salty-moist guy") — there are lots of other words in Cantonese for such fellows, many of them beginning with haam4 sap1 鹹濕 ("salty-moist").
As to why haam4 sap1 鹹濕 ("salty-moist") comes to mean "lecherous", aside from the suggestions that I've already given, there are many other conjectures:
1. In the Qing dynasty, brothels were usually located near the sea, and the air was damp (湿) and smelled salty (咸).
2. The laborers and apprentices who went looking for fun in the brothels were sweaty (湿) and their sweat was salty (咸).
3. The lower-class prostitutes were called "haam4 seoi2 mui6 咸水妹” ("salt water maid") because they lived on the boats and the closeness in pronunciation of "haam4 seoi2 mui6" to "handsome maid" could attract foreigners.
4. "咸" comes from haam4 gwaa3 / Mand. xián guà 咸卦 (Xian trigram) in the Classic of Changes / I ching, where it means "probe".
All of these speculations, especially the latter two, seem far-fetched to me, the last one exceedingly so, since the Xian hexagram (no. 31) actually signifies "influence (wooing)" (Wilhelm / Baynes), not "probing"; furthermore, this ancient usage of xián 咸 ("all; whole; universal; general") has nothing to do with xián 鹹 ("salty").
There is yet another, even more fantastic, idea about why haam4 sap1 鹹濕 ("salty-moist") indicates lechery. According to this article, it was originally a transcription of "hamshop". I suppose that "hamshop" means a shop that sells hams (though I have no idea when that would have been attested in Hong Kong English), but what that has to do with lechery is beyond me — unless it's supposed to evoke the piggishness discussed above.
All right, enough about haam4 sap1 鹹濕 ("salty-moist") in the sense of "lechery". No matter its actual etymology, everybody agrees that it does convey that meaning.
Now, how about "grilled"? I don't see how it can come from any of the three characters, 咸/鹹猪手, that constitute the expression we have been investigating. Rather, I suspect that it was added by the translator to indicate the actual method by means of which pork is commonly cooked in Cantonese speaking areas, namely, "grilling", as in haau1 zyu1 juk6 / Mand. kǎo zhūròu 烤豬肉
For those who wish a more detailed history of the term xiánzhūshǒu 咸猪手 < haam4 zyu1 sau2 鹹猪手 ("groper"), see this article.
To wrap all of this up, it seems that the Chinglish translation compress two meanings — the one figurative and the other literal — to become "Grilled Sexual Harrassment" (this sounds so insane…).
While I'm at it, I might as well also mention that there is another word for sexual harassment that involves a well-known item of food, namely, chī dòufu 吃豆腐 (literally, "eat beancurd"), which is a verb plus noun construction (it is applied thus: "eat [so-and-so's] tofu"). A less colorful verb plus noun construction is zhàn piányi 占便宜 ("take advantage [of so-and-so]").
I hope that I've done justice to David's short but pithy bipartite question with which this blog began.
[Thanks to Bob Bauer, Ranting Jiang, Fangyi Cheng, and Mandy Chan]