This is probably the quickest route to a cease and desist from FB. If you choose this path, you'll need to take a scorched earth strategy because you will not get a second chance. Lots of ways to inject ads into someone else's content, and all of them are against TOS.
It is incredibly unlikely that FB could actually litigate this - it falls under the same legal doctorine that protects ad blockers. Also, a few years ago there was a company called Sambreel that had a product called PageRage. They modified FB pages and inserted ads. Facebook never sued them. In fact, Sambreel actually sued Facebook [1] because the only thing that Facebook could do was pressure advertisers not to work with the company [2], and the company felt wronged. Their lawsuit against Facebook was dismissed, but Facebook was never able to do anything legally against them. One interesting quote from the lawsuit:
"...between July 2009 and October 2010, PageRage grew significantly, and was regularly garnering more than 1 million users per day, and generating more than $1 million in monthly revenues....by mid-July 2011, PageRage had grown to more than 4 million users per day"
In this case, however, there aren't 4M installs. We're talking about less than 300K installs. Facebook would probably not bother with such harsh tactics here.
Regardless of whether they would have legal ground to stand on, it doesn't sound like the OP has the time or money to get into litigation with FB. If they were to send a cease and desist letter, not many people would dig their heels in and take things to the courts out of their own pocket.
