The desperate and angry citizens would be told the fault is the Comstar Leadership, the dead citizens would be used as a bloody flag as they attempt to take over Comstar's assets.
However you're greatly over estimating the effect of taking down Comstar. What you're describing is what would happen if someone waved a magic wand and made all of Comstar's personell and assets disappear.
First the IS nations will be doing their best to capture Comstar assets intact, and when it comes to their more charitable efforts will be successful at that pretty much 100% of the time, so while the funding for the faciliteis may disappear, the facilities themselvs will be there, meaning it's not going to be a case of suddenly the services are unavailable, but of (at worst) gradually less and less services being available.
Second, the vast majority of the lower ranks in Comstar, and pretty much everyone who would allow themselvs to be captured much less be willing to cooperate with the successor states, especially after the discovery of what the upper ranks in ComStar were doing would be highly invested in the charitable operations, so the chances of them dismantling them are Nill, and they'd almost certainly argue against any plan to de-fund them.
Third, in the short term, the successor states need to let former Comstar members keep running Comstar banks and facilities, unless some Blakist managed to destroy evetything of course, in which case the lack of Comstar charities is the least of their worries. In the long term just the economic boost from not having to deal with Comstar would reduce the need for those charities, the improvement in standard of living from improved technology and increased trade would reduce the problems further...well unless all out wart breaks out, in which case again, the lack of charities will be the least of anyone's problems.