The referer header should be spoofed in TBB
Setting network.http.referer.spoofSource
in about:config to true sends the target URL in the referer header. This shouldn't break any websites and it could only be enabled at the safer or safest security settings.
This would stop websites from seeing what website you were previously on from the referer header.
The referer can also be trimmed to reduce the amount of information sent.
A list of all security/privacy related referer options can be found here https://wiki.mozilla.org/Security/Referrer
Trac:
Username: randomname213324