Have you ever seen weirdly shaped lemons or oranges that appear to have 'fingers'? This condition is caused by the Citrus Bud Mite.
It attacks newly forming flowers and fruits. The mite is only visible with a magnifying glass and has a elongated yellow body with four legs that appear to come out of its head. The mites feed inside the buds, killing them or causing a rosette-like growth of the subsequent foliage and distortion of flowers and fruit. The problem is usually limited to just a few fruit on the tree.
Previously recommended oil sprays have not been proved effective. This is one of those pests that is best left alone. The oddly-shaped fruit is edible.
For more information see UC Pest Note on Citrus Bud Mite.