Unfortunately we do not have E*'s motion to read, but by the reading of TiVo's response, it appears E* did not mention the two other elements of the software step: the "audio and video data" and the "temporarily stores." If E* only argued on a single element "parse" I don't see a likelihood of succeeding. One can certainly say the PID filter parses too, just not the kind of parse that has to do with the "audio and video data from the broadcast data," nor "temporarily stores said audio and video data," even though during the hearing E* spent a lot of time on these two elements.
On the issue of "Infringing Products" in the injunction, TiVo argued the same as the judge, that the "Infringing Products" meant for the adjudicated DVRs in their "entirety," meaning both the hardware and software. Because of that TiVo argued even if the new software is non-infringing, it only covers part of the "Infringing Products" and the hardware part is still under the injunction.
But such argument misses the point, if only the new software no longer infringes, the "entire" DVRs no longer infringe, therefore the "entire" DVRs are no longer "Infringing Products," and as such the injuction no longer applies to them.
As I said I believe for the appeals court to stay the order pending appeal, E* must prove there is a very good likelihood that E* can succeed on appeal, nothing else should matter much this time. Without seeing E*'s motion, there is no way of telling what exactly did E* say in there. Will have to wait and see how the appeals court will respond.