I think the invitation to join is for a Private goup membership policy, so they will have been added by the adminstrator before sending the invitation out. For a Closed group the new user requesting membership receives a Welcome email when approved. The Welcome email can be changed (under users and permissions > email).
Thanks for your comments. Having looked into this some more and tried the Private option, it looks as though this is a standard email footer that is added to the bottom of all emails sent by the system (including the one I got telling me you had commented on my question).
The test invitiation email I sent myself that prompted the question includes:
"If you would like to accept this invitation then you can register as a user on the site at:
You will need to specify an email address and password for your new account."
And has the "We have sent you this email as you are a member ..." at the bottom even though it it is suggesting registration.
I think I'll just have to explain the joining process on a web page.
Thanks for your help.