Yes, it is possible to stop hearing your pets responding to orders.
In the Options menu, under the General tab, about two-thirds of the way down in the 'Chat' section, the last option is for 'Pet-Response Text'. 3 options - Only pets you own, Owned and teammate pets, or Disabled.
I think you want the last one.
HTH
Dax Debraxis, Robot Dark MM, lvl 10