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This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2015 The Author Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved ; We conduct a comprehensive numerical study of the orbital dependence of harassment on earlytype dwarfs consisting of 168 different orbits within a realistic, Virgo-like cluster, varying in eccentricity and pericentre distance. We find harassment is only effective at stripping stars or truncating their stellar discs for orbits that enter deep into the cluster core. Comparing to the orbital distribution in cosmological simulations, we find that the majority of the orbits (more than three quarters) result in no stellar mass loss. We also study the effects on the radial profiles of the globular cluster systems of early-type dwarfs. We find these are significantly altered only if harassment is very strong. This suggests that perhaps most early-type dwarfs in clusters such as Virgo have not suffered any tidal stripping of stars or globular clusters due to harassment, as these components are safely embedded deep within their dark matter halo. We demonstrate that this result is actually consistent with an earlier study of harassment of dwarf galaxies, despite the apparent contradiction. Those few dwarf models that do suffer stellar stripping are found out to the virial radius of the cluster at redshift = 0, which mixes them in with less strongly harassed galaxies. However when placed on phase-space diagrams, strongly harassed galaxies are found offset to lower velocities compared to weakly harassed galaxies. This remains true in a cosmological simulation, even when haloes have a wide range of masses and concentrations. Thus phase-space diagrams may be a useful tool for determining the relative likelihood that galaxies have been strongly or weakly harassed ; MF acknowledges support by FONDECYT grant 1130521. RSJ was financed through a Plaskett fellowship. Funding for this research was provided in part by the Marie Curie Actions of the European Commission (FP7-COFUND). GC acknowledges support by FONDECYT grant 3130480. RS acknowledges support from Brain Korea 21 Plus Program (21A20131500002) and the Doyak Grant(2014003730). RS also acknowledges support from the EC through an ERC grant StG-257720, and Fondecyt (project number 3120135). THP acknowledges support by the FONDECYT Regular Project No. 1121005, Gemini-CONICYT Program No. 32100022, as well as support from the FONDAP Center for Astrophysics (15010003). MF and THP acknowledge support from the BASAL Center for Astrophysics and Associated Technologies (PFB-06), Conicyt, Chile. JALA was supported by the projects AYA2010- 21887-C04-04 and by the Consolider-Ingenio 2010 Programme grant CSD2006-00070. JJ thanks the ARC for financial support via DP130100388. AK is supported by the Ministerio de Econom´ıa y Competitividad (MINECO) in Spain through grant AYA2012- 31101 as well as the Consolider-Ingenio 2010 Programme of the Spanish Ministerio de Ciencia e Innovación (MICINN) under grant MultiDark CSD2009-00064. He also acknowledges support from the Australian Research Council (ARC) grants DP130100117 and DP140100198. He further thanks The Lucksmiths for a little distraction. TL, RSJ, RS, and JJ gratefully acknowledge the Aspen Center Of Physics (NSF grant No. 1066293) for their great hospitality, and the valuable service they offer to visiting scientists. SKY acknowledges support from the National Research Foundation of Korea (Doyak grant 2014003730). MAB acknowledges support from the Spanish Government grant AYA2013-48226-C3-1-P and from the Severo Ochoa Excellence programme