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Aims. We investigated the theoretical biases affecting the asteroseismic grid-based estimates of stellar mass, radius, and age in the presence of a mismatch between the heavy element mixture of observed stars and stellar models. Methods. We performed a controlled simulation adopting a stellar effective temperature, [Fe/H], an average large frequency spacing, and a frequency of maximum oscillation power as observational constraints. Synthetic stars were sampled from grids of stellar models computed with different [α/Fe] values from 0.0 to 0.4. The mass, radius, and age of these objects were then estimated by adopting a grid of models with a fixed [α/Fe] value of 0.0. The experiment was repeated assuming different sets of observational uncertainties. In the reference scenario, we adopted an uncertainty of 1.5% in seismic parameters, 50 K in effective temperature, and 0.05 dex in [Fe/H]. A higher uncertainty in the atmospheric constraints was also adopted in order to explore the impact on the precision of the observations of the estimated stellar parameters. Results. Our Monte Carlo experiment showed that estimated parameters are biased up to 3% in mass, 1.5% in radius, and 4% in age when the reference uncertainty scenario was adopted. These values correspond to 45%, 48%, and 16% of the estimated uncertainty in the stellar parameters. These non-negligible biases in mass and radius disappear when adopting larger observational uncertainties because of the possibility of the fitting algorithm exploring a wider range of possible solutions. However, in this scenario, the age is significantly biased by −8%. Finally, we verified that the stellar mass, radius, and age can be estimated with a high accuracy by adopting a grid with the incorrect value of [α/Fe] if the metallicity [Fe/H] of the target is adjusted to match the Z in the fitting grid. In this scenario, the maximum bias in the age was reduced to 1.5%. [ABSTRACT FROM AUTHOR]