looks like you tried to build the thumb using lines.. that's allot more complicated you'll have to make and fill every gap..
Try this...
As the pic shows select the 'bad points' and delete them.
then...
Select the base 'face' as in the pic then 'Extrude' the face 3 times and adjust the positions of the joints using the select point and 'move' tools.
I hope this helps.
Cheers!
P.S. I just noticed a mysterious 'extra' point in the second image you'll need to delete that too.. just make sure all the points 'above' the base face on the thumb part are deleted.