Jake Odorizzi
Another veteran option the Red Sox could turn to on a short-term deal to help out their rotation is Jake Odorizzi. He didn't pitch in 2023 due to shoulder surgery after being traded to the eventual World Series champion Texas Rangers. He's healthy now and threw in front of teams in February. It is unknown if the Red Sox were there.
When he's on the mound, Odorizzi is capable of delivering quality starts, though he hasn't made 30 starts in a season since 2019 with the Minnesota Twins, the lone year he was an All Star. Although minimal, he does bring some playoff experience to the table, as he pitched in the playoffs with the Twins in 2019, the Houston Astros in 2021, and the Atlanta Braves in 2022.
Since the Red Sox were interested in a reclamation project like Giolito, they could do the same for Odorizzi, as he probably won't command a big contract coming off shoulder surgery. While it wouldn't be a super inspiring move, it's worth a shot for the Red Sox in a year where they probably won't go too deep into the postseason, if they make it at all.