A $k$-transmitter $g$ in a polygon $P$, with $n$ vertices, $k$-sees a point $p \in P$ if the line segment $\overline{gp}$ intersects $P$'s boundary at most $k$ times. In the $k$-Transmitter Watchman Route Problem we aim to minimize the length of a $k$-transmitter watchman route along which every point in the polygon---or a discrete set of points in the interior of the polygon---is $k$-seen. We show that the $k$-Transmitter Watchman Route Problem for a discrete set of points is \NP-hard for histograms, uni-monotone polygons, and star-shaped polygons given a fixed starting point. For histograms and uni-monotone polygons it is also \NP-hard without a fixed starting point. Moreover, none of these versions can be approximated to within a factor $c\cdot\log n$, for any constant $c > 0$.