(RP) If w is compatible with the speakers' pragmatic presuppositions in C, then w cannot be properly ignored in C.
Pragmatic presuppositions here are meant to be understood in the Stalnakerian way. The basic idea is that there are different ways to attend to skeptical possibilities; if you just listen to a presentation of them but continue to presuppose them not to obtain, then you can still 'properly ignore' them. But if our common ground shifts so as to include those possibilities, then they are no longer properly ignored.
It may well be that the Rule of Presupposition does a better job with cases than does the original Rule of Attention on the whole. But it does worse in at least some cases. Consider some expression PHI, used to pick out an individual, whose felicity requires that some p be presupposed. For example, the expression "the man sitting at the table" requires it to be common ground that there is a uniquely salient man sitting at a uniquely salient table. Now consider a sentence of the form "PHI does not know q", where p obviously entails q--e.g., "the man sitting at the table does not know that there is a table."
Intuitively (once we've bought into contextualism), some such sentences can both be felicitous and vary in truth from context to context, even when discussing the same subject and proposition. For example, someone in a skeptical context might say "the man sitting at the table does not know that there is a table" truly, even as, in another, nonskeptical context, someone might say "the man sitting at the table does know that there is a table" and speak truly. This is the sort of result contextualists want to capture. But I don't think Blome-Tillmann can capture it. Anybody who utters that sentence felicitously is in a context in which it is presupposed that there is a table. (The previous paragraph gave a recipe for coming up with lots of similar examples.) Blome-Tillman's Rule of Presupposition, then, cannot explain the difference between the skeptical context and the nonskeptical one with respect to whether non-table-including possibilities are properly ignored. And none of Lewis's other rules, besides the Attention one that Blome-Tillman rejects, looks well-suited to do the job either.
So I don't think that presupposition can do the work Blome-Tillman wants it to do in articulating what possibilities are properly ignored. I still think it's best not to get too worked up about these details, and rest content with the contextualist insight.