= Solution
The <mass dimensions> are $[\phi]=1$, $[\psi]=3/2$, $[g]=0$. Up to <total derivatives>, <power counting> allows local <counterterms> of <mass dimension> at most four. A convenient basis for the <counterterm Lagrangian> compatible with the actual <parity symmetry in quantum field theory> and <Dirac fermion number conservation> is
$$
\boxed{\begin{aligned}
\mathcal L_{\rm ct}^{(+)}={}&-\delta\Lambda+\delta Z_\psi\bar\psi i\gamma^\mu\partial_\mu\psi-\delta M\bar\psi\psi
+\tfrac12\delta Z_\phi\partial_\mu\phi\partial^\mu\phi-\tfrac12\delta m^2\phi^2\\
&-\delta g\,\phi\bar\psi\gamma^5\psi-\frac{\delta\lambda}{4!}\phi^4.
\end{aligned}}
$$
The optional constant $\delta\Lambda$ renormalizes the <vacuum energy density>. The <wavefunction renormalization>, <mass counterterms> and <Yukawa coupling> renormalization correct the terms already present. The <quartic interaction> must also be included: the <fermion loop> with four external bosonic legs is logarithmically divergent, even if the <renormalized> quartic coupling is set to zero at one chosen <renormalization scale>. The displayed original interactions alone do not form a closed set of <counterterms>.
If “most general” is interpreted before imposing the <parity symmetry in quantum field theory> examined in <1/d>, <Lorentz invariance>, a <Hermitian> <action> and <Dirac fermion number conservation> also allow
$$
\begin{aligned}
\mathcal L_{\rm ct}^{(-)}={}&-\delta t\,\phi-\frac{\delta\kappa}{3!}\phi^3-\delta y\,\phi\bar\psi\psi-\delta M_5\bar\psi\gamma^5\psi
+\delta Z_5\bar\psi\gamma^\mu\gamma^5\partial_\mu\psi.
\end{aligned}
$$
Here all coefficients can be real in the paper's <gamma matrix> convention; the last term is Hermitian in the <action> up to a <total derivative>. It is an axial kinetic normalization, which could alternatively be removed by a suitable perturbative field redefinition. Every term in $\mathcal L_{\rm ct}^{(-)}$ is odd under the actual <parity symmetry in quantum field theory>, so its coefficient vanishes in a symmetry-preserving <renormalization scheme>. Listing these terms makes explicit which assumption excludes a <tadpole counterterm>, a cubic scalar term, a scalar <Yukawa interaction>, a pseudoscalar <Dirac mass term> and an axial kinetic term.
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