Oh come on. You want to tail her, not taze her.
They probably don't realize that Grace isn't the carrier.
Well, depends on how the authors are going to fill the plot hole: the church (and their opponents) had the means to track down Maggie (and her predecessors) out of the blue but aren't able to dig her up in the camp right now. Did they have a mole or canary at the conception and tailed her from there by conventional means? If so, why wait for the pregnancy to proceed? Because it's easier tracking one target for a while instead of having to find deal with the next one right away?
In page 20 of chapter one, you see the Church finds the carrier through pregnancy checkups / blood screenings. Maggie was posing as Grace (for insurance fraud, lol) so the Church thinks Grace is the carrier. After Kurt goes psycho at the abortion clinic and shoots/kills several people (including Maggie), they lament later about Clancy's intel sucking and the carrier (presumed by Clancy to be Grace) not being there.