The Aussie was also undermined by news one of the countries' major banks had nudged up its variable mortgage rate, adding to pressure on the Reserve Bank of Australia (RBA) to cut official rates.
The Aussie faded away to $1.0722, from $1.0787 in New York and a six-month peak of $1.0845 earlier in the week.
The New Zealand dollar followed to $0.8307, from $0.8334 on Thursday and a five-month high of $0.8408.
News that Greece had finally agreed a deal on a bailout drew only muted cheers from the market and was largely priced in.
The Australian currency had been on the rise since Tuesday's decision by the RBA to keep rates at 4.25 percent, confounding market expectations of a cut to 4 percent.
But, with the market already very long of the currency, it struggled to sustain gains above $1.0800 and then took a knock when China reported a drop in both exports and imports for January. China is Australia's biggest export market and any hint of weakness tends to hurt the Aussie.
The decline accelerated when Australia and New Zealand Bank announced it was raising its variable mortgage rate by 6 basis points to compensate for higher funding costs.
"It's clear than bank funding costs have risen and if more do pass on those costs to customers in a broad-based way that will tend to tighten financial conditions in the economy," said Paul Bloxham, head of Australian economics at HSBC.
"If the RBA then judges that conditions are tightening too much it will respond by cutting the cash rate," he added.
Investors duly reacted by narrowing the odds of an easing in coming months. Interbank futures imply around a 54 percent chance of a cut in March and are now fully priced for a move to 4 percent by April.
The RBA itself had sounded comfortable with where rates were for the moment in its quarterly statement on monetary policy, a 70-page assessment of the economic outlook.
Bond futures also recouped a little of the hefty losses suffered since Tuesday. The three-year contract edged up 0.070 points to 96.460, having previously struck its lowest since mid-November. The 10-year contract added 0.045 points to 95.925, off a two-month trough of 96.875.
The yield curve has still flattened markedly this week, with the spread between three- and 10-year yields around 54 basis points, compared to as much as 72 basis points last month.
NEW ZEALAND DOLLAR
The kiwi dollar remains almost 7 percent higher this year, but is looking a bit tired after it failed to sustain gains above $0.8400.
"The kiwi continues to move tantalisingly close to key levels but unable to produce the momentum to break either," said ANZ senior dealer Alex Sinton.
"Topside strategic sellers are looking a little more medium term and expecting some disappointment when the dust begins to settle around the Greek debt solution."
Traders said offers above $0.8400 would cap near-term gains for the moment, while support was seen around $0.8285, the low on Feb. 6.
The kiwi was unmoved by data showing electronic retail card sales rising a seasonally adjusted 1.2 percent in January, ending two months of falls.
The euro edges up to A$1.2357 on the Aussie, off a low of A$1.2124. It was last at NZ$1.5944, against a record low NZ$1.5627 hit earlier this week.
New Zealand government bonds were a shade lower, with yields as much as 3 basis points higher.