I think you should assume they have made the mistake until told otherwise. Always write back mentioning Phoebe, and let them pick you up on it. When they do, say 'OMG I am SO sorry, it's just that it is usually spelt Phoebe so I just assumed that's what it was.'
Variant my eye.
I think it's most likely settled into common(ish) usage because of people just plain getting it wrong.
I would write Phoebe. (And cringe for the child if that is what the parents have really done but I think it's more likely a grandparent not familiar with the name thinking OE couldn't possibly be the right order for the vowels and correcting the parents' spelling). It won't be the last time someone spells it right.
There are people who have spelled their own kids names wrong, you see them on here sometimes. Pheobe has been spotted on this very forum, poster was not happy when it was pointed out.
Impossible to know whether thats how they spelled it or if the granparents just got it wrong. Personally I'd just write it the proper way, tough bollox to them if they got it wrong, they'll have to get used to it coming up!
I think it's a pretty common mispelling, but more likely to be a mistake by the gps than the parents (though not impossible, and also possible that they just thought it "looked nicer" or was "more unik" that way).
Do you usually send a card to the parents? I think you could get away with just saying something like "congratulations on your new arrival" or "lovely news about the new arrival / new addition" etc.
It's a distant cousin of DH's - I haven't seen them in about 6 years and have no idea of their phone number. We're not at all close to that branch of the family, and DFIL is utterly hopeless at anything to do with communication (hence us not even knowing their was a baby in the offing!).
I'm inclined to think it's a spelling mistake on the grandparents' part. If it isn't, i'm guessing this may be something the child deals with a lot in the next few years!
We've received a Christmas card introducing their new grandchild Pheobe. I now have to write a card back congratulating them on said new arrival. At first glance I assumed they'd written Phoebe wrongly, then I googled and it is apparently a variant of Phoebe, though I've never come across it before. Do i go with their spelling as written in the card and risk offending them if they think I've misspelt it, or do I write Phoebe and risk offence for getting it wrong?!