By Gromov-Witten K-theoretic invariants (call them KGW) I mean the invariants defined by Givental and Lee.
I expect the formula expresses the KGW of the generic fiber of a given degeneration in terms of the KGW of expanded pairs as well as non-rigid expansions, in the style similar to K-theoretic WDVV equation, i.e. an alternating sum where the number of factors corresponding to non-rigid expansions is arbitrarily many.
In fact, I only need to deal with the following situation:
(1) $g=0$,
(2) the normal bundle of the divisor in each of the pairs is trivial, and
(3) the contact order of curves with the divisor is always 1.
In this case, the relative KGW should be equal to absolute KGW.
