Can you please provide additional information?
Is the neighbor simply contacting the board to say that they feel uncomfortable having strangers in the building? Or does the behavior meet the legal definition of stalking (this is the US one): “Whoever engages in a course of conduct (using mail, electronic communications, or travel across state lines) with the intent to kill, injure, harass, intimidate, or place under surveillance, and which causes the victim to reasonably fear death, serious bodily injury, or substantial emotional distress.”
If the latter, I would definitely contact an expert on stalking and follow their advice. This will likely be a mental health expert. In many cases, unfortunately, involving the police only escalates the behavior.
Be very clear on the outcome that you want and ensure that whatever course of action you take will increase the chances of that outcome occurring.
I cannot envision any scenario where blocking their access to THS will make any difference.
However, if the neighbor is simply contacting the board to say that they feel uncomfortable having unaccompanied strangers in the building, that is a different scenario altogether. In that case it seems reasonable that they would show “evidence” from THS that you are having people stay in the building while you are away.
I have occasionally sat for a couple in another country whose “strata board” (they have a different name) has firm rules against having guests at the property for more than three nights in a row, regardless of the arrangement (AirBnB, friends, family - anything). This is partly because they are in a prime location in a major city and the full-time residents experienced significant disruption from tourists. Officially my being there for a week taking care of the cats is a violation of the rules, and I am incredibly careful to be “invisible” and quiet. So far no one has complained, but if a neighbor did not approve of my presence, I could easily see them doing what yours is doing to say, Hey, we have rules. This has to stop.
There is not enough information in your post to ascertain what the neighbor actually wants. However, most stalkers don’t involve a strata board. A neighbor who is worried that a variety of strangers will have access to the building, however - that neighbor might contact the strata board. And I would have sympathy for that neighbor.
If the “neighbor worried about strangers in the building” is closer to your scenario, might it be possible to have a chat with them and help them understand the THS vetting process? If they think that you just post a listing and whoever raises their hand first gets to stay, of course they will be worried. But if they understand that you get to review the sitter’s previous sits, have a video conversation with them, etc., that might set their mind at ease.
If, however, they truly are mentally ill and are threatening you with harm, speaking with them will make it worse. In that case, contact an expert and follow their advice.
Please let us know how this turns out.
P.S. @Mark_B and @Jenny: We have learned the hard way that post titles steer the discussion dramatically. Might it be possible to retitle this thread, “Neighbor sharing my THS listing with Strata board”? - at least until the OP can provide additional information? That seems a more accurate representation of what is occurring with the H.O.