Oh, I'm sure Elves never had a squirrel "problem". They probably had a deep and abiding respect and love for squirrels, not for any particular use squirrels may have had, but simply as living creatures different from themselves, unique in their own squirrel-ness, an expression of the grand Theme of Ilúvatar, which gave Shape to the World.
And, squirrels probably made pretty good targets for bow practice.