Of course... the other question you could also ask yourself is whether you'd have the bard make a Charisma (Lute tool) check, or a Dexterity (Lute tool) check... since playing an instrument such as that requires more hand-eye coordination than it does personal magnetism or strength of character.
If we assume that the Tool proficiency the bard has is for lute (since every instrument has its own separate Tool proficiency), then I'd usually use the Tool proficiency for the check. Although there's a pretty good chance it doesn't really matter, because the bard's going to be proficient in Performance and the Tool proficiency anyway, resulting in the same bonus.
. . . use a tool (organ) check.


(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.