You would have to provide a termination lug(s) in the box. You will have to provide lug(s) suitable for the connection of four grounding conductors, one from each grounding bushing and one from each conduit.
If the EGC in the raceway it equal to or larger than the specified bonding jumper between the grounding bushing and the box, you could land the internal EGC on the grounding bushing and continue that same conductor to the termination on the box.
A couple of notes to the above after re-reading the question.
If they are using the raceway as the EGC, there would be no EGC in the conduit. If there is an EGC in the raceways, and if the ungrounded conductors pass through the box without a splice or termination, the EGC would also be permitted to pass through the box without being terminated.