Frankie mouse and Benjy mouse are two white mice who belong to Trillian.
They escaped from Earth before the premature termination of its program. Mice are not, as is commonly assumed on Earth, small white squeaking animals who spend a lot of time being experimented on. In fact they are hyper-intelligent pan-dimensional beings who are searching for the ultimate question. It is this search that led to the creation of the Earth.
We'll make you a reasonably rich man.Frankie mouse
At first they intend to get the Magrathean's to rebuild the Earth in order to complete the experiment. However in the end they ask Arthur to find them the ultimate question so that they can make lots of money on the talk show circuit.
The whole business with the cheese and the squeaking is just a front.