I haven't been able to find independent verification, but APOPO does have relevant information on their website:
- 19,650 Landmines destroyed
- 88,251 UXO destroyed
- 23,623,426 [m2] Safe land returned to communities
The Washington Post article was written two years ago in 2017, while APOPO was founded in 1997. This information is more current than that.
The claim's "100,000+ mines" refers to both landmines and unexploded ordnances, which together currently total 107,901. These numbers also seem to be for the entire company, not just the rats. There are several steps that need to occur before the rats are even put to work, including clearing the area of growth and creating safe lanes for people to walk on, where explosives have to be detected by people with metal detectors. The rats only help find the explosives and are not responsible for detonating them. The explosives are safely detonated by people when no person or rat is close enough to get hurt.
According to a peer-reviewed paper written in part by people at APOPO, the rats don't work the entire day, so people end up doing some of the demining:
The main disadvantage of rats is that they do not work well when it is extremely hot and sunny. Therefore, in warm weather—which is characteristic of Gaza Province—demining with the rats is limited to the cool of morning. Later in the day, handlers shift to other activities, such as clearing brush and manually demining. Although pouched rats play an invaluable role in APOPO's mine clearance activities, they are by no means the sole weapon in the arsenal.
Another relevant peer-reviewed paper (with essentially the same authors) about the efficacy of these rats was was published:
The rats searched a total of 93,400 m2 in 2009, and this land was subsequently made available for the use of local people. The rats located a total of 41 mines. Humans with metal detectors found no mines beyond those located by the rats.
(Also "54 other explosive devices" were found during the period studied in the paper.)