Apertureless near-field microscopy is an imaging technique in which a small metal tip is held close to a surface, converting evanescent waves to propagating waves and permitting sub-wavelength spatial resolution. In the terahertz region of the spectrum, the interpretation of measured signals and the suppression of background scattering can be complicated by the broad bandwidth of the THz source and by the phase-sensitive detection of the scattered radiation. We have analyzed the use of tip-sample distance modulation for the removal of background signals. We find that significant background signals, originating from scattering off the probe tip, can be observed even after modulation. These background signals result from path-length difference modulation, and thus depend on phase-sensitive detection. We use a dipole antenna model to explain the spatial variation of this signal. Since it originates from the tip only, it can be used to characterize free-space terahertz wave fronts with sub-wavelength resolution.