The apparent consensus is that
"extra damage" is
intended only to apply to
"damage rolls," and any damage bonus that does
not specificly apply to
"damage rolls," but
"damage dealt" and so on, has been
misworded.
As currently written in the
PHB Errata:
“Once per round, when you hit your quarry with an attack, the attack deals extra damage based on your level.”
Other than the
Errata above only places
"extra damage" is explictly called out in the
PHB is similar wording for the
Rogue and
Warlock, extra damage granted on a critical hit,
PHB278, and extra damage granted by a magical weapon,
PHB225.
"Extra damage" is not mentioned under
Hit, PHB57, only
"modifiers to...damage rolls," nor is it mentioned under
Damage, PHB276.
As
written, the
"extra damage" granted by
Hunter's Quarry appears to apply whenever damage is dealt by a successful attack roll. However, most read
"Extra damage" as
implicitly a
"bonus to damage rolls," in which case it would not apply to
Furious Smash.
Absent further
Errata, perhaps my partner would be interested in taking up your case, as I am currently deeply involved in litigation regarding
Fleeting Ghost. But this represents the current understanding as practiced in the player community.
Yours sincerely,
Smeelbo, Axam, & Veagar
Attorneys At Law
"Reading the rules with a fine tooth comb since 1975."