Mit Käse spart man Mäuse

This is a slogan by McDonald's here in Switzerland. Translated straight it means with cheese you save mice. ??? Am told it's a word joke. But I think it's so "clever" that most Swiss I have asked do not understand the funny bit. Guess it's meant to mean how cheap they are. Since "Mäuse" could mean money.

All I can think of is if I'm eating rat meat when dining in McDonald's? Not quite sure that was the meaning of the ad...