What are the white tendrils at the bottom of these garlic cloves?
Those are garlic roots, no reason to worry.

If you plan to use these cloves, note that they are about to leave the dormant stage and start to sprout, so make sure you remove the green sprout in the middle of the clove. It is rather likely to have turned bitter now. 

I found this video on youtube, which shows the roots forming on a garlic clove; in a rather early stage you can clearly see the little stubs your garlic has.