These are various images showing variations in grip and wrist angles with different types of sword. The earliest images are from the late 13th century and the last from the mid 16th century. The grip variation may be used for various reasons; to gain more strength in the bind by reinforcing against the flat with the thumb, or changing the balance of the sword by gripping the cross with the index finger.

Especially the Talhoffer images are interesting in my opinion, since a few images show both the thumb and index finger held straight in an open grip.

A couple of more things of interest in Talhoffer: One of the images of duelling shields in the 1459 manuscript shows a kick against the shield, where the attacker causes the shield to spin open, thus creating an opening.

Another image from the 1467 manuscript appears to show a left-handed cut against the legs, although I may be misinterpreting it. I will have to check the sequence more properly.

It is hard to know if the "open" grips were common and not properly portrayed in many illustrations or more of a personal preference amongst certain swordsmen. But, another thing that came to mind is Myamoto Musashi's advice to grip the sword with two fingers only.

Reading the quote from Musashi, it seems quite similar to what we see in some of the plates from Talhoffer.

And in relation to this, Peter Johnson's (and others) discussion on gripping a viking sword is interesting.