You can use them while holding the straps in your fist, like a buckler.
When the shield is constructed right you can use it quite effectively like that.
There are some similar examples -
this one has two horizontal bars that would hold strap and add some rigidity to the shield (I'm assuming these are orginal)
A very similar one is in Nuremberg, but you can't see the backside of it in the exhibition.
This one I posted quite a while ago in a thread about the construction of these "grooved" shields:
I could add a few more but that's not the point of the thread, I guess
I have no idea what the groove originaly was for. In Tom B.'s link you can see them strapped to an arm but considering that the same design was used with much larger shields that you could not strap to your arm I doubt that this is the intention for the groove. Some shields still exists that don't have a groove but are angled, I posted one of them.
The few extant grips are made from bovine leather or rawhide. Some reproductions use tightly wound rope an I used leather straps covered in rope (as a stand-in because I lacked the heavy gauge leather or rawhide used in the originals). As long as the grip is pretty stiff it does not seem to matter.
€dit:
This original one uses a wood grip covered with leather!
