After migration to Exchange 2013 from 2003 I seem to have transferred an email address that was attached to a public folder to a system rolegroup. The public folder was deleted and not migrated.  I cannot find the email attribute in ADUC for the group but can find it using

get-adobject -filter {mail -like helpdesk@laver.co.uk"}

CN=Help Desk,CN=Microsoft Exchange System Objects,DC=laver,DC=local
Name - Help Desk
ObjectClass - Public Folder
ObjectGUID - 400027e5-83df-4e2c-af16-64f5d32384b5

How do I remove this email address from the rolegroup (which thinks its a public folder) so I can use the SMTP address again

get-adgroup "help desk"

DistinguishedName : CN=Help Desk,OU=Microsoft Exchange Security Groups,DC=laver,DC=local

GroupCategory     : Security

GroupScope        : Universal

Name              : Help Desk

ObjectClass       : group

ObjectGUID        : 730c40e8-e379-4c2c-86a9-35c7ca5adc0f

SamAccountName    : Help Desk

SID               : S-1-5-21-513294795-2120549601-927750060-12670

• Edited by wildingc Wednesday, August 13, 2014 9:20 AM typo

Regarding:

get-adobject -filter {mail -like helpdesk@laver.co.uk"}

the filter is finding the public folder object in AD, the object that holds the e-mail address and causes the mail to be routed to public folders.

Regarding:

get-adgroup "help desk"

I don't see evidence in your post that this group is mail-enabled and has an address.  Run Get-DistributionGroup and see if it shows up.