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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 extreme subwavelength spatial resolution. This technique has recently been adapted for use in the terahertz region of the spectrum. Here, the interpretation of the measured signals and the suppression of background scattering can be complicated by the extremely broad bandwidth of the terahertz source and by the coherent (i.e., 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 are relevant when phase-sensitive detection is used. We use a dipole antenna model to explain the spatial variation in the scattered signal. Since this signal originates from the tip only, it can be used to characterize free-space terahertz wave fronts with subwavelength resolution.