  The repeating fast radio burst FRB 20200120E is located in a globular cluster
belonging to the nearby M81 galaxy. Its small distance (3.6 Mpc) and accurate
localization make it an interesting target to search for bursting activity at
high energies. From November 2003 to September 2021, the INTEGRAL satellite has
obtained an exposure time of 18 Ms on the M81 sky region. We used these data to
search for hard X-ray bursts from FRB 20200120E using the IBIS/ISGRI
instrument, without finding any significant candidate, down to an average
fluence limit of $\sim10^{-8}$ erg cm$^{-2}$ (20-200 keV). The corresponding
limit on the isotropic luminosity for a burst of duration $\Delta t$ is
$\sim10^{45} \left ( \frac{10~ms}{\Delta t} \right )$ erg s$^{-1}$, the deepest
limit obtained for an extragalactic FRB in the hard X-ray range. This rules out
the emission of powerful flares at a rate higher than 0.1 yr$^{-1}$ that could
be expected in models invoking young hyper-active magnetars.
