Tinderbox, from v8.0.2, anonymously reports some simple usage statistics to help Eastgate make features easier to discover, and to understand what languages and which versions of macOS are actually used by Tinderbox users. This is controlled via the Tinderbox Preferences/Register dialog.
Eastgate collect only very general features, such as what kinds of views are being used or how frequently tabs are deleted. Such indications about how users use the app, and which parts they use (few use every feature).
As a long-lived app (born 2001) and as a multi-purpose tool there are a lot of small features added because someone had a real need for it. Often these become obsolete (or simply unused). It can be helpful for a small company like Eastgate to understand how best to prioritise limited resources to best serve its users.
No identifying personal information and no information about the content of a document's notes is transferred. Care has been taken to ensure that this will not impede work when offline or when the server is busy.
The default setting (In Preferences/Register) is set to opt in (un-ticked). Tick the box if you don't want information to be shared. This might be a generic personal privacy point of view, or because of use on a network whose organisation's rules dislike or ban such background features.
However, aTbRef's author strongly advises allowing sharing unless you have a specific reason not to. It can only help make Tinderbox better.