It's not a phrase I've ever heard before.

Breaking it down, in case you're curious:

"Seasoning" (you're doubtless aware) refers to salt and pepper, and the act of adding them to food. But I've never heard the word "seasoner" to refer to a salt or pepper dispenser.

The "table" part is fairly commonly used as in "table salt" i.e. salt in a dispenser on the dining table. It's also occasionally used in phrases like "water for the table" when asking a waiter to bring enough water for everyone at the table.

But "table seasoners" is a bit over-laboured for me.