The Twins should have some leverage here. Boston really wants to cut payroll before the season starts and LA needs mookie for their all in push especially after already trading Joc Peterson. The Twins should threaten to walk away.
I actually think LA has the most to lose. They're the team that everyone is most excited for regarding this trade.
If the Twins threaten to walk I think there's a good chance LA lets them and they make up for Graterol with something they previously weren't willing to part with.