Like most adjectives in English, "any" does not have a grammatical number. It works with countably singular nouns. It works with uncountably singular nouns. It works with plural nouns.
The pronouns "it" and "them", however, do have grammatical number. The pronouns "he", "she" and "it" are all singular. The pronoun "them" is plural.*
Please let me know if there is any problem.
Please let me know if there are any problems.
These sentences work. In the first, the form "is" agrees with its singular subject. In the second, the form "are" agrees with its plural subject.
If there is any scooter or bike parked in front my door, I will throw it away.
If there are any scooters or bikes parked in front my door, I will throw them away.
Both of these sentences work. The "it" refers to the singular "any scooter or bike". The "them" refers to the plural "any scooters or bikes".
If there is any book that is better than yours, it is this one.
* If there are any books that are better than yours, it is this one.
There is a problem with the second sentence of this pair. In the first, "any book" is singular, and the pronoun "it" refers to this antecedent. In the second, "any books" is plural, but "this one" is singular. The pronoun "it" has no clear antecedent, but we have reason to use some singular form. One way to fix the problem is to use a different pronoun:
If there are any books that are better than yours, this is one.
Of course, another way to fix the problem is to simply use the first version of the sentence. It's easier to keep grammatical number in agreement when only one number is relevant.
* The use of "they", "them" and "their" to represent a singular person without reference to gender is gaining popularity. Even so, we still use "it" for singular things and "they" form plural things. The so-called singular they only works for people.