Joint message and state transmission under arbitrarily varying jamming is investigated in this paper. The problem is modeled as the transmission over a channel with random states with a fixed distribution and jamming that varies in an unknown manner. We consider cases in which the channel state is known at the encoder strictly causally and noncausally. For each case, both the average error criterion and the maximal error criterion of the message transmission are adopted. The main results of this paper are lower bounds of the capacity-distortion function of the aforementioned scenarios. The proposed coding schemes are deterministic, and no correlated randomness is needed to achieve reliable communication and estimation. The gap of bounds caused by different error criteria is illustrated by a numerical example.