This is why soldiers are NOT supposed to care for/take in wild animals while deployed. This dog could very well be carrying diseases or any number of other pathogens, possibly ones that we don't have here in the US. This can be an endangerment to the health and well being of deployed troops. This dog could also now apparently compromise a mission. There is a special published directive that gets written up for any deployments called General Orders. One of these orders that are emplaced prohibit troops from taking in wildlife. Not to mention that we have enough animals here in the states already that are not being cared for, why bring another here? The wildlife there, while deployed, is best left alone. Or at least left behind for the next troops to take care of.
While deployed to Iraq we used to catch wild hedgehogs, camel spiders, scorpions and snakes. (One of the snakes was a black desert cobra.) We would return them to the wild though away from troop areas. Dogs and cats were for the most part put down on site by the base QRF.

Not trying to be a jerk or anything but there are reasons why General Orders should be followed, besides the fact that they are Lawful Orders punishable by UCMJ action.