I think H. Pussey, as a seller and publisher of toys & games, used Grimaud as the manufacturer of its cards.
Another of the card decks advertised in the booklet that comes with the H. Pussey is
Le Nouveau Grand Jeu de la Main, which was published by H. Pussey c.1880-1890.
An edition was also published by Grimaud in 1890 (there is a copy on view at BnF)
However, an edition of this (c.1900?), has both B. P. Grimaud on the box, and H. Pussey as vendor (of Toys & Games).
So I think possibly the H. Pussey was the first, published by him but manufactured by Grimaud; and then later Grimaud published their own version?
B. P. Grimaud at the top, and in the red ribbon at the bottom
Jeux et Jouets H.PUSSEY M.ROLLIN succ.
The above was sold at auction, the seller's description:
L'Avenir dévoilé par le Nouveau Grand Jeu Chiromancique », par Madame Adèle MOREAU (élève de Mlle LE NORMAND, fabrication B.P.GRIMAUD, contenant 56 cartes et 7 couleurs avec la notice et l'étui d'origine. Vendu par la Ste Jeux et Jouets H.PUSSEY (M.ROLLIN succ.)(circa 1900)
"The Future unveiled by the New Great Palmistry Game" by Mrs. Adele MOREAU (student of Miss LE NORMAND, manufacture by B. P. GRIMAUD, containing 56 cards in 7 colors with manual and original case. Sold by Games & Toys H.PUSSEY (M.ROLLIN succ.) (circa 1900)
Another of those advertised in the accompanying booklet to his Etteilla I is
Le Petit Oracle des Dames. There is a copy of a
Le Petit Oracle des Dames that was published by Pussey (the name H. Pussey is printed on the court cards) in the British Museum.
