People don’t “get offended at anything these days.” Had the word used been “slimeball” none of us would have thought twice about it. But look up the word “greaseball” (not “greaser”) in any slang dictionary and you will see that it is an ethnic slur.
From the dictionary: " Noun 1.greaseball – (ethnic slur) offensive term for a person of Italian descent." Of course, it has also been used for decades against Hispanics. What was the cartoonist thinking—unless the strip has Rosa dump him for using such language? A nerd is fine to date; a thoughtless bigot is not.
The toon would be more understandable had the two children not looked Asian.