When I switch to the full size view to see the social network media and go to "me", I can see all my old personal messages I posted the last three months but I can't delete them. The cog shows me just a link with (useless) "more options". Since the whole Live Profile pages are scrubbed there's no way to find elementary settings like these on the new Microsoft account pages as well. I hope this will be fixed soon or you have a helpful advice to solve this issue. 

note: Terms may be incorrect, I use the German country setting.