The app they are running is in fact a near clone of an app sold by a company who personally trained the authors of the clone. The app does use patented technologies. So from a legal standpoint, there is little chance this app and its company will survive the suit. One possibility for successful defense would be software patent law unexpectedly collapsing during litigation due to a surprise ruling by SCOTUS on some other case. This is a long shot. Another possibility would be the defending party countersuing, challenging the validity of the patent and succeeding. This is possible, but expensive to do and will take many years. Even if they succeed overturning the patent, it will still be challenging to prevail overall, given their intimate association with the patent holder and likelihood of existing contracts between them.

So what to do in the meantime? Normally what would happen is the plaintiff would seek the judge to issue an injunction against sales pending trial, which would have to prove there is a high likelihood they would prevail in the litigation.

This is being skipped because of the App Store situation, where there is a gatekeeper able to remove products from sale for arbitrary or even nonexistent reasons. The existence of these stores, free from competition (they certainly can not go to the Amazon iPad store and download the software there because Amazon isn't allowed access to install iPad apps therefore there is no competition and Apple has a monopoly on running iOS software stores) is a large threat to software and customer freedom.

I agree this is a really bad situation, but it is one that Apple customers voluntarily accept when they buy products for this platform, and that developers accept when they develop products for this platform. It's like buying a house with an authoritarian Homeowners Association that is capricious and issues fines for painting your fences the same color as before without paying $2200 to the History, Style and Architecture Review Committee to have a public hearing to review and approve your fence painting plans. It is no secret the system exists or how it works, and persons subjecting them to the whims of others in these situations know what they are getting into and accept the terms.

So what to do? Many things are possible. Here are a few.

1. As has been mentioned, disable all updates, turn off wifi, use this iPad only for this app and buy another iPad if you want to update it.

2. Purchase the multi-thousand dollar version on custom hardware published by the plaintiff. (Presumably insurance companies normally pay for this option.)

3. Jailbreak the iPad and convince the program's authors to release a jailbroken compatible version.

4. Convince the publisher to relocate outside the US in a country that does not recognize software patents this encompassing and sell the program on the Android pad platform.