UPDATE: I asked JAXA, and here's what they told me (it's along the lines of what we all expected):
Current version of data processing makes an erroneous bias of
sea ice extent on June 1st and October 15th which are seen
in the graph of sea ice extent as a small blip on these dates.
The apparent bias arises due to a switching of some parameters
in the processing on both dates. The parameter switching is
needed because the surface of the Arctic sea-ice becomes
wet in summer due to the melting of ice which changes
satellite-observed signatures of sea-ice drastically.
We are planning to improve the processing to make the gap
much smoother soon.