In the following sentence does "beyond your comprehension" have an offensive connotation?
When a large population of tourists swarm the city during the tourism season, it's beyond your comprehension.
In the following sentence does "beyond your comprehension" have an offensive connotation?
When a large population of tourists swarm the city during the tourism season, it's beyond your comprehension.
If you are directing it at a particular person it may be somewhat offensive, since it implies that they are stupid. It would be better to say, "... is beyond comprehension" In other words it is beyond anyone's comprehension, not just yours.
In the actual context, I can comprehend a very large number of tourists, so I'm not sure that the expression fits well.
No. It's not offensive, although beyond your comprehension can be used in an offensive way.
Italian is beyond your comprehension, could be considered offensive if it implies you are not smart enough to learn a new language.
Your usage, however, describes an event that your audience/listener has never experienced. In that case saying that it's beyond their comprehension is not a comment on their intelligence or wisdom but instead an observation that their experience would be unique.
It might best be expressed, When a large population of tourists swarms the city during the tourism season, it will be beyond your comprehension. This further clarifies that you're not making an assumption about someone's abilities but instead about their experiences.
In the sentence quoted in the question, depending on the context, 'your' is possibly used in the same meaning as 'one's' (i.e., it is the possessive form of generic you):
When [...], it's beyond one's comprehension.
In that case it is not offensive. Rather, it is very similar to "it's beyond comprehension".
As used in the OP:
In the following sentence does "beyond your comprehension" have an offensive connotation?
When a large population of tourists swarm the city during the tourism season, it's beyond your comprehension.
A native speaker would almost certainly not take offense to hearing that the population of tourists was "beyond your comprehension". Although some of my fellow native speakers seem to have little faith in the average person's intelligence, average people perfectly well understand what it means to exaggerate for effect, and also what the generic you means.
They would take "beyond your comprehension" as a hyperbolic overstatement meant to convey the sheer size of the crowd, and the "your" in that phrase as referring not to them in particular, but as a colloquial synonym for "one's", i.e. "beyond one's comprehension".
So yes, you could use this sentence without fear of offending any but the most "dedicated offense-seekers" (as @Marquis puts it in a comment).
The example sentence sounds like a miss-translation. Since it is not really targeted I would guess most people understand it as a bad idiom for "unbelievable".
In German for example is the "das kannst Du Dir nicht vorstellen" (you can’t imagine..). This would be better translated with "you won’t believe it" or "beyond ones comprehension".
As for the precise question, if you use the term in a sentence like "This topic is beyond your comprehension" this would be incredible rude or condescending, you would basically call the other person stupid - your sentence seems not be meant like this, however it can be easily misunderstood, so better avoid it.
I don't know the context for the original quote, but it sounds to me as though someone has failed to prepare for the arrival of large numbers of tourists in tourist season, and someone else is suggesting that the first person is incapable of understanding that this was a likely occurrence.
If so, since it's hardly a difficult thing to anticipate, implying that someone is too stupid to anticipate it is highly offensive.
To solve this general problem, you can use the word "incomprehensible" instead. The passive voice means it's not a specific indictment of the reader's ability to comprehend; rather, it's a judgement about the entire world.
However, that would still read rather oddly in your sentence. You could instead refer to the "incomprehensibly vast swarm of tourists during the high season", for example (where I've used "vast" so as to avoid implying that the tourists are incomprehensible - e.g. that they can't speak the native language).