Hi C.
I had the same problem with my daughter, she is now 5 months old and she used to scratch her face right under her eye (this freaked me out) trying to get her thumb in her mouth. I asked her doctor what I could do to avoid this happening, and she said that all I can do is keep her nails trimmed, and that she would learn how not to miss her mouth. And she has! Now what she does is she will use her other hand as a guide for her thumb hand to her mouth (no joke, even her doctor saw this), she will put her whole hand in her mouth and take fingers out until she just has her thumb in there, lol. She has it down to a science. It is a sight to watch that. But you are exactly right, it is more soothing to them than a binkie. This is why I do not try and stop her from doing it right now while she is a baby. My mother tells me I should stop her but it is soothing to her (and me), lol. Hope this helps. Jess