It's giving her an interest in life.
It's distracting her attention.

Without saying a word about John Gilman it is making her see for herself the weak spots in him through the very subtle method of calling her attention to the strength that may lie in another man.

For once in your life, Linda, you have done something strictly worth while.

The thing for you to do is to keep it up, and in order to keep it up, to make each letter fresh and original, you will have to do a good deal of sticking around Peter Morrison's location and absorbing rather thoroughly the things he says.

Peter doesn't know he is writing those letters but he is in them till it's a wonder Marian does not hear him drawl and see the imps twisting his lips as she reads them.
Before I write another single one I'll go see Peter.