Do you work on your child's irrational fears?

If your child has/had any overwhelming or irrational fears do you work with them to help them overcome it? The neighbor girls (5 and 3) came over to play yesterday and apparently didn't know we have a dog. As soon as they laid eyes on our 15 lbs. geriatric rat terrier (who was just standing there) they both began screaming and crying hysterically (no exaggeration)(you'd have thought there was a mountain lion in the house). I put the dog in another room and asked their mom if they'd had a bad experience with a dog and she said they hadn't. Anyways...I found it odd and wondered what parents do/have done if their child had such an overwhelming fear of something or if they just let it go.