This behavior is actually by design. The reason:
My main goal when designing the Clono integration, was for it to work "out of the box". With no need for opening (and learn using) the Clono admin panel. Linking to live games from the TS web pages, and fetching results back from the tablets, was completely automated with no \user action required except ticking the checkbox to activate clono integration inside TS. If something went wrong, the easy fix for any problem would then be to untick the check box and then tick it again, to create a fresh tournament at the clono end. Yes the clono T_ID would change but TS handles all those details behind the scenes, so the change wouldn't matter - except if bookmarked/old links elsewhere pointed directly to the previous clono pages.
However, not all tournaments fit this straight forward model. Some games may be played without tablet/clono. Some games may be played on lichess. Some games may have no integration except manually created PGN files. But the main reason for having to manipulate stuff inside clono panel is the changes introduced in clono for 2 tablets per board and the "favourite tablet" setup, which breaks the (old but working) auto-assignment of tablets from TS. The latter is something I hope to iron out together with Clono, if they have time and interest.
But the most interesting use-case for further development is tournaments like this where multiple integration technologies (i.e clono and Lichess) are in use at the same time. Real-world inputs like yours is therefore indispensable, so please mail me details about your setup, experiences and further needs (wish list) if you can find the time.
Anyway: I have reconsidered this behavior and upcoming releases of TS will keep the clono GUID and T_id even if clono integration is momentarily turned off. When turned on again there will be a popup msg asking if a new or existing clono tournament should be connected. Hopefully that cover most scenarios.