Clad in a burgundy baby doll dress, she’d slipped on a tongue-in-cheek accessory—a black baseball hat emblazoned with Posey’s quirky twang; “Piper, nooo. Tsunahhhmi. Bewdisuhm. Noooo.

The hat giveaway to Boston Public Schools students began in 2017 in partnership with JetBlue, the official airline of the Boston Red Sox, to connect baseball to the next generation of fans. “Hat Day ...