An old sense of the verb hark (which mainly means to listen) was used in hunting with hounds, where the phrase hark back denoted the act of returning along the course taken to recover a lost scent.1 This is the origin of the modern sense of hark back, which means to recall, to return, or to retrace one’s steps.
Hearken and harken also mean to listen. In fact, the three words are essentially the same, coming from the same Old English root and having an archaic tone in modern usage. But unlike hark, hearken and harken weren’t used in that hunting sense, so hearken back and harken back don’t work the same way.
Still, hearken back and harken back appear often. In edited news publications, though, hark back is about three times as common as harken back and about five times as common as hearken back.
These writers use hark back well:
The lo-fi pop rock of the Black Lips harks back to frantic surf-guitar hits from the early sixties. [New Yorker]
Speaking of past expiry dates, Ms. Glover’s political tresses clearly hark back to the heady days of the 1980s. [quoted in Winnipeg Free Press]
The Conservatives are harking back, he said, to the “politics of division” practised by Margaret Thatcher during the 1980s … [Irish Times]
In each of these examples, hark back could replace the alternatives:
Their line defence is outstanding, but their ruck defence hearkens back to last year’s interpretation. [Telegraph]
That harkens back to a time when the Uptown neighborhood was a hillbilly heaven with many blue-collar families who relocated from the South. [Chicago Sun-Times]
Come to think of it, even today’s fascination with electric cars harkens to the turn of last century … [Stuff.co.nz]
Still, the fact that harken and hearken are so widely used (and, in these examples, by editorially scrupulous publications) suggests we should consider them accepted variants of hark. After all, they’re harmless. And the words are rarely used in other contexts, so there’s no chance of confusion.