They filed the trademarks some months ago: http://www.macrumors.com/2014/05/30/healthbook-healthkit-tra...
I don't think Apple is too concerned. If HealthKit had filed for trademarks internationally then they'd have a leg to stand on.
Instead they're left moaning about how Apple has named some technology, not a packaged product per-se, with a name similar to their company.
Apple's legal team was no doubt aware of HealthKit, had done some analysis, and decided that there was no real issue. HealthKit can do their thing in Australia.
A few years ago DC Comics decided to sue DC Shoes over their logo which, like DC Comics logo at the time, used the letters DC and a star.
Turns out DC hadn't trademarked the logo, despite having used it (and variants) for decades so they lost.
DC Shoes HAD trademarked it and successfully counter sued and DC Comics, despite having used a similar logo for a lot longer, were forced to pay DC Shoes for the rights (at least until they ultimately changed their logo).