The answer is "the pool."
The expression "in their backyard" is a prepositional phrase, which modifies the noun before it.
Prepositional phrases are words arranged without a subject or verb. They are usually made up of either a preposition and a noun, a preposition and a gerund, or a preposition and a clause.
If prepositional phrases modify a noun, as in this case, they are called "adjectival phrases."
