Prevent a Notify rule response going to another organisations 'auto-reply'

Prevent a Notify rule response going to another organisations 'auto-reply'

Here is the situation:
- we send an email to a support@ email address via Ticket A
- they send us an auto-reply saying 'thank you for your email' to our support@ email address, it creates Ticket B
- our Notify rule then sends them a response to their support@ email address saying 'thank you for your email, we have created Ticket B for you'
- they then send us another auto-reply saying 'thank you for your email' to our support@ email address, it creates Ticket C
- our Notify rule is execute again...

And so on and so on until we have many new tickets created for the auto-replies from the other organisation.

How can we prevent this from happening? We want to receive the first auto-reply from the other organisation, but don't want our Notify rule to be executed.