They have admitted an "oversight" after complaints from Islamic residents who consider dogs "ritually unclean".
Six-month-old trainee police dog Rebel is at the centre of the row.
The German Shepherd was pictured next to a police hat and telephone on a card highlighting the Tayside force's new non-emergency contact number.
Thousands were sent out to addresses in the Dundee area.
But Muslims were angry and their local councillor raised their concerns.