Since you're bringing up "capturing the data", it's worth pointing at Kagi's privacy policy, the very first point of which is this:

> * Searches are anonymous and private to you. Kagi does not log and associate searches with an account.

https://kagi.com/privacy

Additionally the search page itself displays this notice:

> Your searches are always private. We do not see them and they are not associated with your account

The "captured" user data you seem to be concerned about doesn't appear to actually exist in this case; the data is quite explicitly not being captured.