Disabling auto emailing to specific mail accounts

Disabling auto emailing to specific mail accounts

tl;dr 

Another support company we email have an automatic reply to say "Thank you for contacting us" 
then we email them back with an automated response saying "Thank you for contacting us"
then they reply back to say "Thank you for ....

etc. etc.


Is there a way to stop this for particular email addresses? 
If not, please could you look at doing this? 

Thank you
Brad
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