Thank you for you response. Following your suggestion, we inquired a reseller of Maple T.A. and were told that the newest version, Maple T.A. 2016.1, can be configured to return the Highest / Average / Last grade via LTI. We plan to upgrade because this satisfies our demand.
Although the upgrade would solve our problem completely, I imagine an alternative design of Moodle External Tool module, the LTI consumer. Assume that there is only one grading item on an LTI provider. Students use the external tool repeatedly, say, once a day. The external tool module, if appropriately designed, could record the last grade returned, a single integer, in its own database table every time a student attempts the tool. Then the module could calculate the Highest / Average / Last or some statistical quantity from the table entries and send it to the Moodle gradebook, just like the Quiz module does. This could add more flexibility for the case where the LTI provider only returns the last grade.