Now that the app is actually out and we can see what it does, the Tzomet institute has an article about it. In summary, they say it is forbidden. They take issue with the app's primary claim, which is that the app utilizes a time delay and calls this a grama. The Tzomet institute (which is a pioneer in the development of grama based devices and has some serious halachic and technological knowledge), utilizes both time delays and indirect causation in all of their grama switches.
According to the publishers of this application, the Halachik basis for this leniency is a time delay between the human action and the electrical response. All Orthodox rabbis, including the most liberal, are well aware that every human action, that has a desirable outcome, is strictly forbidden even if it has a delayed response and even if it takes place only after a certain time. A person initiating a delayed mechanism is considered as if "shooting an arrow", where the results are attributed directly to this person’s action.
In our 'Gramma' mechanism, when a person presses a button or a touch screen, they do not start any chain reaction – 'shooting an arrow'. This indirect activation ('Gramma') is based on a complex technological design and the result is not a chain reaction started by a human hand. As stated before, our 'Gramma' solutions are for medical and security use only.
Then they add in a few more issues just for good measure:
Another aspect of this issue, is that while communicating with someone else, a person also activates electrical circuits on the second persons phone. All this is without even mentioning anything about the Melacha of writing, the 'Image of Shabbat', the importance of a Shabbat atmosphere and the Halachik aspects of Shabbat such as 'Uvdin D’Chol' and 'Maris Ayin'. There is no need to further explore these concepts in order to completely prohibit this surreal and absurd so called Shabbos app.