  Gravitational-wave memory is a non-linear effect predicted by general
relativity that remains undetected. We apply a Bayesian analysis framework to
search for gravitational-wave memory using binary black hole mergers in
LIGO-Virgo-KAGRA's third gravitational-wave transient catalogue. We obtain a
Bayes factor of $\ln \text{BF}=0.01$, in favour of the no-memory hypothesis,
which implies that we are unable to measure memory with currently available
data. This is consistent with previous work, suggesting that a catalogue of
$\mathcal{O}(2000)$ binary black hole mergers is needed to detect memory. We
look for new physics by allowing the memory amplitude to deviate from the
prediction of general relativity by a multiplicative factor $A$. We obtain an
upper limit of $A<23$ ($95\%$ credibility).
