"Secret menu" is usually a term used for services not advertised, not for provider availability. I can tell you when I worked at a legal brothel in NV my profile was always up, even when I was not there. If you then contact the brothel and say you want to make an appointment with Scarlet, you would be told "she is not here right now, but XYZ is available who looks similar and provides the same services." Even when there were only 4 or 5 gals working there were always 20-30 profiles listed. This agency may have all of their providers listed in TER but on their website only show who is available that day or week.

When you click on a Provider link in the TER Profile, you are getting the complete link, such as:
agency.com/models/scarlet123 (or sometimes directly to a photo .../scarlet123/scarlet001.jpg).
Scarlet's page and photos are still on the agency's server, so Scarlet's page is displayed using the complete, direct link.
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When you go directly to the agency.com home page, you only see what their server serves you, e.g.,  
agency.com (home page) [Welcome] [About] [Models] [Calendar] [Rates] [Blog]
You click on [Models] which opens
agency.com/models with links or linked-photos of [Alice] [Betty] [Cindy] ... but no [Scarlet]
The agency removed "scarlet" from the agency.com/models page so you no longer see a link to the  
agency.com/models/scarlet123 page even though it still exists.
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Removing or deleting the [Scarlet] link on the agency.com/models page could be as simple as "commenting out" that line of code:
agency.com/models/scarlet123 = [Scarlet] active / displayed
[Comment on] agency.com/models/scarlet123 [Comment off] = [Scarlet] INactive / NOT displayed  
(TER does not allow HTML in posts so I can't type greater-than, !, double dash in this actual post. Anything between [Comment on] code and [Comment off] code is treated as a comment and is not processed or displayed.)
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When Scarlet comes back, the webmaster can just delete the [Comment on] and [Comment off] around the link to Scarlet
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There are probably better, easier ways to manage the active / inactive links on the "models" page, but that is why you can still see the Provider's page and photos still on the agency website from the direct COMPLETE link on TER but can't see the Provider's page and photos beginning from the agency home page.  
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It is NOT a secret menu. It is a way to manage their website. Comment out a model when she is not available; display the model's page when she is available without having to recreate the model's  "personal" web page.

I think what's happening is that all the model profiles are kept on the website, which is why you can see them individually via a direct link on a TER review profile. However, not all the models are available at the time, so the website temporarily hides the pictures and links to the ones who are not available. When the models return, they simple re-activate their links. It makes website maintenance a lot easier.

A very common web page management technique.  Not necessarily a 'secret menu'.

 
From a website maintenance perspective, it is easier to have all of your pages created in advance.  Then, when a page is needed (e.g. a provider becomes available), you simply add a link for the pre-existing provider page to the 'Available Now' page seen by clients, by creating a link to the pre-existing page.  Similarly, when a service (provider) becomes unavailable, you simply remove the link from user's view.

 
However, the pages themselves continue to exist and are accessible by navigating to the address directly.