We present an analysis of the sensitivity
of LHC searches for new spin-0 particles
produced via gluon-fusion and decaying into
top-antitop-quark ($t\bar{t}$) final states
to generic axion-like particles (ALPs)
coupled to top-quarks and gluons.
We derive new limits on the effective ALP
Lagrangian in the linear representation
in terms of the Wilson
coefficients $c_{t}$ and $c_{\tilde{G}}$
based on the existing
CMS search using $35$ fb$^{-1}$ of proton-proton scattering data collected
at $\sqrt{s} = 13$ TeV.
We further investigate posssible distinctions between ALPs and pseudoscalar
Higgs bosons as predicted by the Two Higgs doublet model (2HDM), and
find that a distinction is possible
with data anticipated to be collected
during the high-luminosity phase of the LHC
for a significant range of the effective ALP-gluon coupling.