Probably no reason to undertake the bother of removing the blooms. And you certainly don't want to cut or damage any spur shoots that some of the flowers may be growing from.

After the tree is mature some pruning of old spurs may become part of the routine, but on a new tree you want to keep all of these. On a related note there may be a case for preventing new and small apple trees from fruiting until after the tree has built up a top with some size to it. In this instance you would snip off any apples that start to form, again without damaging the spur shoots these are growing from.

If it indeed is Granny Smith, then no worries; it's tough as nails and will fruit in the spring again. The tree knows what to do. Here it never does go dormant, but keeps its leaves all winter and the new ones push the old ones out in the spring (so much for the dormancy theory) and fruits just fine.

Applenut

I have a golden delicious that is doing the same on one limb. I don't think it will hurt anything.

I have several newly planted apples that bloomed off season. I forgot about the spurs, I snipped some of the blooms.

Speaking of Granny Smiths, can someone explain to me why so few people let Granny Smith ripen to what they are supposed to be -a yellow, very sweet dessert apple? Ours ripen in January, and they are simply delicious. But I don't care for the green ones.

Why do you think apples are supposed to be sweet?
GS has been described as a tart green cooking apple since it was discovered.

There's a lot of green apples that will hold until they are overripe and yellow or blushed.
I could leave my Cortland on the tree until they rot.
That doesn't mean that's what they're supposed to be.

Now I don't buy that argument. You can take almost any apple and pick it when it's green and it's ok to cook with, provided the flesh is dense enough not to fall apart once cooked. But that doesn't mean you're getting the best cooker. And on the other end of the spectrum, there are many green apples that are supposed to remain green, for example, Rhode Island greening, and they deteriorate in flavor if not picked on time. But this is absolutely not the case with Granny Smith which continues to improve in flavor and texture.

The Granny wasn't always known to be a green cooker. My fellow Australian friends inform me that there, it's known to be a sweet apple, and it's many children's favorite apple. And I've spoken to countless apple farmers who grow it and remarked the same oddity - how wonderful of a table apple it is, yet people buy it when it's green and one dimensional. And the, it's not what I would call a good cooking apple, it becomes rather bland. By the way, a ripe Granny Smith isn't just sweet, it's a very rich blend of sweet and sour and so multi-dimensional that it makes you wonder why anyone would pick it green.

Now I don't think apples should all be sweet. I grow Allington Pippin for example, it stays tart, and it's a great cooker. And so is Belle de Boscop. Now I also happen to like tart apples and I eat my Allingtons and boscoops right off the trees. BTW, none of these sweeten up, they hold their tartness until they finally drop from the trees and go mushy or who knows what. This is not the case with Granny Smith, which continues to improve in flavor.

Granny Smith is categorically not a cooker by default, it's only a cooker because it's picked way before it's ripe.

Here it is the 2nd of October and I've got one that's blooming, too. :) I suspect it's because we went through a rough drought this summer, and only just recently received a decent amount of rain which jump started the growing season again. And it's not just the apples. Several plants that managed to pull through the drought and should have been done making by now (under normal conditions anyway) have suddenly put on a showcase of blossoms. Lot of good it will do now though, since we usually get a killing frost about mid October.