Needs["xAct`xTensor`"]

$PrePrint=ScreenDollarIndices;

DefManifold[M4,4,Complement[IndexRange[a,z],{g,h,k,q}]]

DefMetric[-1,g[-a,-b],CD]

DefTensor[F[-a,-b],M4,Antisymmetric[{-a,-b}]]
DefTensor[η[a,b],M4,Symmetric[{a,b}]]
DefTensor[h[LI[q],a,b],M4,Symmetric[{a,b}]]
DefConstantSymbol[k]

L=g[a,c] g[b,d] F[-a,-b] F[-c,-d];

ruleIG=MakeRule[{g[a,b],η[a,b]-k*h[LI[q],a,b]+k^2*h[LI[q],a,c] h[LI[q],-c,b]-k^3*h[LI[q],a,c] h[LI[q],-c,-d] h[LI[q],d,b]},MetricOn->All,UseSymmetries->True];

L/.ruleIG
%//ToCanonical