The District of Columbia in Contingent Presidential Elections

Suppose a presidential election ends in a 269-269 tie. That would a trigger a contingent election in the House of Representatives with each state getting one vote. (This last occurred in 1825.)

In that contingent election, the District of Columbia would not be represented. This is strange given that the District chooses presidential electors and would be, by necessity, essential for triggering the contingent election. I wonder if the Framers of the 23rd Amendment considered this problem, overlooked the issue because contingent presidential elections are rare, or might have said that the District should be treated as a state with voting rights in Congress in this singular circumstance.