  Mass and distance are fundamental quantities to measure in gravitational-wave
(GW) astronomy. However, recent studies suggest that the measurement may be
biased due to the acceleration of GW source. Here we develop an analytical
method to quantify such a bias induced by a tertiary on a double white dwarf
(DWD), since DWDs are the most common GW sources in the milli-Hertz band. We
show that in a large parameter space the mass is degenerate with the peculiar
acceleration, so that from the waveform we can only retrieve a mass of ${\cal
M}(1+\Gamma)^{3/5}$, where ${\cal M}$ is the real chirp mass of the DWD and
$\Gamma$ is a dimensionless factor proportional to the peculiar acceleration.
Based on our analytical method, we conduct mock observation of DWDs by the
Laser Interferometer Space Antenna (LISA). We find that in about $9\%$ of the
cases the measured chirp mass is biased due to the presence of a tertiary by
$(5-30)\%$. Even more extreme cases are found in about a dozen DWDs and they
may be misclassified as double neutron stars, binary black holes, DWDs
undergoing mass transfer, or even binaries containing lower-mass-gap objects
and primordial black holes. The bias in mass also affects the measurement of
distance, resulting in a seemingly over-density of DWDs within a heliocentric
distance of $1$ kpc as well as beyond $100$ kpc. Our result highlights the
necessity of modeling the astrophysical environments of GW sources to retrieve
their correct physical parameters.
