You shouldn't have a problem. The website and phone app are buggy, and I wouldn't worry at all about what they say. When you check-in at the counter, just be sure your bags are tagged to your final destination. If they aren't automatically, just point out your final destination to the TA to have it fixed.

These were likely booked correctly, but the computer is simply confused when it comes time to display them. But, rest easy -- even if these were booked as three separate DL tickets, you wouldn't have a problem getting the TA to check to your final destination.