How to deal with someone who has a grudge against you?

My best friend made a joke about dogs at his workplace a couple months ago. He did not tell me the exact joke, but it was not directed towards anyone or anyone’s pet in particular.

One of his acquaintances, another friend of mine, overheard the joke (this acquaintance was from a different department but happened to be passing by on an errand). This “acquaintance” (let’s call him Joe) was notorious for posting pictures of his two dogs all over his cubicle and for occassionally sending pictures of them to his colleagues (including my best friend). Joe was immediately offended by the joke, glared at my best friend while passing by, and stopped talking to my friend altogether.

Now, my best friend’s department and Joe’s department started working on a project together. So far, Joe has given my best friend a cold shoulder, responding to his greetings with simple grunts or sometimes total silence. Joe has so far not voiced any displeasure regarding the joke and is known to be a sensitive individual (so maybe he was upset about something else).

Would it be a good idea for my best friend to address the joke with Joe and perhaps apologize? My best friend’s joke was not directed at Joe and he in fact did not even know that Joe was around until it was too late. On one hand, my friend wants to put the past behind him but on the other hand, my friend fears that addressing the joke issue might spark an argument.