Ghoul Retainer and Jar of Skin Eaters

Can Ghoul Retainer use Jar of Skin Eaters if it has zero blood on it?

Name: Ghoul Retainer
[Jyhad:R2, VTES:R, CE:R2, KoT:U/R]
Cardtype: Retainer
Cost: 2 pool
Ghoul with 2 life. 1 strength.
During the initial strike resolution each round, the Ghoul Retainer inflicts 1 damage or may use a weapon not used by the employing minion (or another retainer) that round (either before or after). This is not a strike, although it does count as "using" the weapon.
Artist: L. A. Williams; Richard Thomas

Name: Jar of Skin Eaters
[HttB:C]
Cardtype: Equipment
Clan: Tremere/Tremere antitribu
Weapon.
The bearer may use this weapon only if it has a blood on it. Strike: 3R aggravated damage. This minion may inflict 3 aggravated damage on another minion as a action. Burn after either use. Any Gargoyle enslaved to this vampire may move 1 blood to this card as a +1 stealth action.
Artist: Erica Danell

And what about the part of: "Burn after either use.", but the ghoul retainer says: "or may use a weapon not used by the employing minion (or another retainer) that round (either before or after). This is not a strike, although it does count as "using" the weapon."

The question is: "is burned the Jar of Skin Eaters after be used by the ghoul retainer?"