The central engine of a gamma-ray burst (GRB) is widely believed to launch a pair of oppositely moving jets, i.e., the forward jet moving toward us and the counter jet regressing away. The forward jet generates the radiation typically observed in GRBs, while the counter jet has not been detected yet due to its dimness. GRB 170817A, a short burst associated with a binary neutron star merger event, is a nearby event (z = 0.0097) with an off-axis structured energetic forward jet and hence probably the most suitable target for searching the counter jet radiation. Assuming the same properties for the forward and counter jet components as well as the shock parameters, the fit to the multiwavelength afterglow emission of GRB 170817A suggests a peak time ∼quite a few ×103 day of the counter jet radiation, but the detection prospect of this new component is not promising. Anyhow, if the shock parameters (ϵ e and ϵ B) of the counter jet component are (a few times) higher than that of the forward shock, e.g., the posterior results of the magnetic energy fraction of the forward shock and the counter jet are log10ϵB =−4.23−0.69+1.42 and log10ϵB,cj =−3.65−2.11+3.06 , respectively, as still allowed by the current data, the counter jet afterglow emission will be enhanced and hence may be detected. A few hours of exposure by JWST in the F356W band will stringently test such a scenario.