How to delete an address, phone, email, or website in a profile?
I recall this coming up a number of times on the old Forum and the answer was 'can't be done'. And I thought this was going to be an unhelpful answer but Post 1 took me to Post 2 which took me to this Include ID when editing 'block' fields (+ allow deletion of block values via Profiles) which is flagged as Fixed for 4.7.

What version are you on? Want to go test on master