Actually, also curious if the organization has gotten any such warnings or concerns raised, as I'm sure there's no way they don't at least know about what's gone on and him being questioned, etc. .
Since with missions trips and organizations there is nearly always screening that takes place (plus background checks of some sort - though often more informal not "real" police/fingerprint types) they'd probably have learned stuff through that, too.
Typically it's quite extensive, especially for people going on a longer term mission trip or one term (vs. just shorter term ones - whether that's a week or two or even a few months) And that rarely means not putting everyone through that, no matter their title/past experience or training, etc.
Often they include personality tests/assessments, some degree of psychological testing and meeting with a counselor/therapist/or at least a pastor for assessment, character statements/references, personal interviews, and usually some sort of candidacy program - all of that nearly always required for anything even remotely longer term.
Very small organizations it's a little less common, though, or at least that extent.
In this case, however, since he's known to them from having worked with them before, it's possible that any earlier screening could be accepted (and if they had no issues w/ him prior) that then they might not go through whatever measures along those lines they may have in place. However even that tends to be the exception and not the rule.
I can't imagine they aren't aware - at least to some extent - of what's gone on since surely they asked about his personal life, if nothing else just out of social niceties.
I wouldn't think that it could be out of the question that they may find themselves getting some major pressure from people now that word is getting out about his plans, perhaps even from people also serving within this organization/ministry.
In fact, there's a blogger who's had some significant controversy in her past, and her husband as well who saw something similar impact their lives/plans. To a larger extent it's technically on him, though she made false accusations and has since acknowledged that, so it's all a little fuzzy - but that's not really the point other than to indicate it's a situation that's similarly not cut and dry as to the truth, as is the case w/ what's gone on w/ Karen - though this is also significantly more serious as far as possible charges/involvement)
Anyway, the organization got A LOT of concerns raised, comments, people saying they'd no longer associate with them, etc. if they chose to let the husband still be involved, and they looked into it and decided that regardless of the truth (which may never be known) that the controversy alone wasn't something they wanted or something that would reflect well on their mission of serving the Lord, nevermind on the reputation of their organization.
I wouldn't think that is out of the question to see happen in this case, as well.
If nothing else, and even if they believe he's entirely innocent in Karen's death - and I'm not stating that I'm assuming he is involved one way or another - I'd imagine that they'd insist he undergo some degree of counseling of some sort to ensure that they feel he's in a healthy enough place to actually be effective in the ministry, etc. Especially since cross-cultural work brings a whole new set of pressures and stress, even if it's a place you know and can communicate well in, etc (none of which there's any indications are true of him as far as living in Frankfurt) and you're typically away from your support system and all of that.