Optical observations of blue compact dwarf galaxies (BCDs) show they typically have high specific star formation rates black (sSFRs) and low metallicites. A subset of these galaxies (those with the lowest gas phase metallicities) display cometary optical morphologies similar to those found at high redshift. Whether this combination of properties predominantly arises from interactions with neighbours or via accretion from the cosmic web, or is indeed due to something else, remains unclear. Our aim is to use high-resolution mapping to gain insights into the processes driving the observed properties of a sample of extremely metal-poor (XMP) BCDs. We present Very Large Array B-- and C--configuration mapping of the four BCDs of our sample. For three of the targeted BCDs, we also detected and mapped the in their nearby companions. In these three cases, there is morphological and kinematic evidence of a recent flyby interaction between the BCD and a nearby companion galaxy. The evidence for recent interactions for these three BCDs is corroborated by our analysis of the tidal forces exerted on the BCDs by companions with available spectroscopic redshifts. In one of these cases, J0204--1009, we obtain sufficient spatial resolution to determine that the BCD is dominated by dark matter black (DM) and estimate its DM halo mass to be in the range of 1.2 times 1011 to 5.2 times 1011 However, it is the most isolated BCD in our small sample, J0301--0052, that shows one of the most asymmetric morphologies . J0301--0052 has a similar cometary morphology to its optical morphology, although the column density maximum is projected at the end of the optical tail. Our observations suggest that J0301--0052 may be undergoing a merger, while the other members of our BCD sample show evidence of a recent tidal interaction with a near neighbour. While our selection criteria favour BCDs with companions, our results are consistent with previous literature showing that most BCDs are associated with either mild tidal interactions or mergers.