The measurement and characterization of the lensing of the cosmic microwave background (CMB) is key goal of the current and next generation of CMB experiments. We perform a case study of a three-channel balloon-borne CMB experiment observing the sky at (l,b)=(250deg,-38deg) and attaining a sensitivity of 5.25 muK-arcmin with 8 angular resolution at 150 GHz, in order to assess whether the effect of polarized Galactic dust is expected to be a significant contaminant to the lensing signal reconstructed using the EB quadratic estimator. We find that for our assumed dust model, polarization fractions of about as low as a few percent may lead to a significant dust bias to the lensing convergence power spectrum. We investigated a parametric component separation method, proposed by Stompor et al. (2009), as well as a template cleaning method, for mitigating the effect of this dust bias. The template-based method recovers unbiased convergence power spectrum in all polarization fraction cases we considered, while for the component separation technique we find a dust contrast regime in which the accuracy of the profile likelihood spectral index estimate breaks down, and in which external information on the dust frequency scaling is needed. We propose a criterion for putting a requirement on the accuracy with which the dust spectral index must be estimated or constrained, and demonstrate that if this requirement is met, then the dust bias can be removed.
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