I think you have presented a wrong perspective of Tabligh-jamat. I know the ideals of the Jamat. They never entertain and or show any political inclination. I have never been associated with Tabligh-jamat but I'm aware of the ideals of the Jamat.
They always talk about life here and life above (heaven). It is not possible to do a background check before a person joins Tabligh-jamat.
How can the Jamat be held responsible when some or few individual do any terror related (un-Islamic) activity?