We present an X-ray morphological and spectroscopic study of the pulsar B2224+65 and its apparent jet-like X-ray features based on two epoch Chandra observations. The main X-ray feature, which shows a large directional offset from the ram-pressure confined pulsar wind nebula (Guitar nebula), is broader in apparent width and shows evidence for spectral hardening (at 95 per cent confidence) in the second epoch compared to the first. Furthermore, the sharp leading edge of the feature is found to have a proper motion consistent with that of the pulsar (∼180 mas yr−1). The combined data set also provides evidence for the presence of a counter feature, albeit substantially fainter and shorter than the main one. Additional spectral trends along the major and minor axes of the feature are only marginally detected in the two epoch data, including softening counter to the direction of proper motion. Possible explanations for the X-ray features include diffuse energetic particles being confined by an organized ambient magnetic field as well as a simple ballistic jet interpretation; however, the former may have difficulty in explaining observed spectral trends between epochs and along the feature's major axis, whereas the latter may struggle to elucidate its linearity. Given the low counting statistics available in the two epoch observations, it remains difficult to determine a physical production scenario for these enigmatic X-ray emitting features with any certainty.