Motivated by the generalization of the Maslov index to tube domains and by numerous applications of related index function in infinite-dimensional situations, we describe in this paper a topologically oriented approach to an index function generalizing the Maslov index for bounded symmetric domains of tube type to a variety of infinite-dimensional situations containing in particular the class of all bounded symmetric domains of tube type in Banach spaces. The framework is that of 3-graded Banach--Lie groups and corresponding Jordan triple systems.