  A number of open problems hinder our present ability to extract scientific
information from data that will be gathered by the near-future
gravitational-wave mission LISA. Many of these relate to the modeling,
detection and characterization of signals from binary inspirals with an extreme
component-mass ratio of $\lesssim10^{-4}$. In this paper, we draw attention to
the issue of systematic error in parameter estimation due to the use of fast
but approximate waveform models; this is found to be relevant for
extreme-mass-ratio inspirals even in the case of waveforms with $\gtrsim90\%$
overlap accuracy and moderate ($\gtrsim30$) signal-to-noise ratios. A scheme
that uses Gaussian processes to interpolate and marginalize over waveform error
is adapted and investigated as a possible precursor solution to this problem.
Several new methodological results are obtained, and the viability of the
technique is successfully demonstrated on a three-parameter example in the
setting of the LISA Data Challenge.
