Hello -- you wrote this query some years ago (before I became admin of this Board) but I just came across it and thought I would reply anyway.
As far as I can determine, there is/was no location called Bettreds in Kent or elsewhere in England. It's possibly a mis-spelling of another name/location. For example, I found no mention at all of any Bettreds on the GENUKI website (UK & Ireland Genealogy) here http://www.genuki.org.uk
However, a Google search did turn up about ten mentions of Bettreds on various websites (including some comments that it's a castle). But they all seem to be a repetition of the same details you have posted here, ie. I think it's a case of the same erroneous info/spelling being shared by various researchers and posted in various places.
Having said all that, though, I could be wrong. I suggest that you post a query on the Kent-ENG mailing list. It has hundreds of subscribers, many of whom are very knowledgeable about Kent history & geography. Maybe someone there can provide an answer. If you need info about finding that mailing list, let me know. Regards, Andrea (Kent Board admin)