AI could have charged OP the excess baggage fee through to MSP rather than just to DEL, and then DL would have gone to AI to collect their tariff rather than charging OP twice. That would have (in theory) alleviated the issue OP is facing in that he was charged 2 times.

However, a) that would have been more expensive as AI is less generous with excess baggage fees, and b) DL might have decided not to honor the payment and charge its own baggage fee anyway.

So I think that OP got the best deal he could with the least complications.. But certainly, excess baggage interlines is something which airlines should establish clearer rules and policies for.