Why does the Grumman Bat feature inverted winglets?
Without knowing what was going on in the minds of the designers it's difficult to tell exactly, however there are a few reasons as to why the vertical stabilizers are featured both above and below the wing.

In the sUAS market there are a huge amount of products which offer very similar capabilities. It is quite possible that the stabilizer design of above and below rather than in a single direction is to differentiate the product in a crowded market. This is similar to business jet design wingtip design - while it is known drag may be reduced the devices offer aesthetic appeal and different designs stand out to buyers. 

The design also allows for the same surface area with a smaller packing footprint. Due to the bulbous shape of the fuselage the potential package size of the bat is smaller with the stabilizers as designed rather than simply above or below.

The stabilizer design is symmetric around the horizontal plane, meaning that in a side gust condition the UAS will feature less tendencety to roll and will instead simply be 'shifted'. 

Again in a side gust condition the balancing of forces above and below the attachment point cancels out the moments and therefore may allow for a less strong joint (weight savings).