From Jar-Jar to the Anakin/Obi-Wan rivalry to Padme's absolutely wooden dialogue... There's nothing of value in that scene at all, IMO. So my solution was to just ditch it. Now we transition from Mace saying "I'll have Obi-Wan report to you immediately, M'Lady" to an exterior of Padme's apartment at night (stolen from ROTS). And then "You look tired..."
From there, everything we need to know is explained and it excises things like "I don't think she liked me watching her."