  In this paper, we consider compatible Hom-Lie triple systems. Compatible
Hom-Lie triple systems are characterized as Maurer-Cartan elements in a
suitable bidifferential graded Lie algebra. We also define a cohomology theory
for compatible Hom-Lie triple systems. As applications of cohomology, we study
abelian extensions and deformations of compatible Hom-Lie triple systems.
