@jeremiahwk cards are in an evolving state right now. You may notice experiments being run. There are quite a few inconstancies while data is gathered that will help determine what approach is best for the web and mobile. The below is in regards to mobile only.
The link is removed to give the Tweet a simpler appearance. This is inline with other cards types. If the URL is in the middle of text it is assumed the URL is giving some textual context to the Tweet and it is retained.
Where you may see other inconstancies is in the timeline. The AppCard URL remains in the timeline no matter what. This is because AppCards are not expanded in the timeline and the user needs something to click on. Other cards like the Summary Card are expanded in the timeline and the link is removed in timeline and in details view.