Quality of RF Power Splitter
Does this mean an additional 2.6dB is lost to heat within the power splitter?


Or there is a reflection back toward the generator.

Or there is some radiation from the splitter (this is unlikely to account for all of the excess loss you measured if you paid more than $1 for the splitter).

Did you measure \$S_{11}\$ when you had the thing on the VNA?

When you measured \$S_{21}\$, did you terminate port 3 properly?


  What kinds of modifications can I make on an off-the-shelf power splitter to solve this issue?


If the additional loss is a problem for your setup, your best bet is probably buy a better splitter.

If the problem is due to reflection, you could conceivably improve the performance with some kind of matching transformer. If the problem is resistive or radiative loss, buying a better splitter is probably the only realistic choice.