Is this possessive optional? How would it affect the meaning of the sentence?

Solution 1:

At the risk of launching a pedantic discussion of band names that start or don't start with the (or The) . . .

Arctic Monkeys is the name of the band; there's no the (or The) involved.

For the sake of comparison, let's take another band with a non-the (or non-The) name, but in this case singular: Metallica.

I went to see the Metallica concert last week. (ok)

I went to see Metallica's concert last week. (ok)

*I went to see the Metallica's concert last week. (not ok)

Do you see where this is going?

I went to see the Arctic Monkeys concert last week. (ok)

I went to see Arctic Monkeys' concert last week. (ok)

*I went to see the Arctic Monkeys' concert last week. (not ok)