The word mudra covers three bodies of material that get printed together and are neither the same age nor the same kind of thing. The iconographic layer is a hand position that identifies a figure in sculpture and painting, readable from the early centuries CE onward. The textual layer is the mudras named in the hatha and tantric corpus, where a mudra is a whole bodily technique rather than a hand shape. The third is a twentieth century therapeutic literature of finger positions matched to elements and ailments, which borrows the vocabulary of the other two and is continuous with neither.
Gyan Mudra belongs to the second layer. Jnana mudra is named in the hatha corpus, so it belongs to the textual layer rather than to the iconographic one. It also sits at the centre of a genuine and unresolved disagreement: Jnana and Chin are described by different sources as the same seal, as mirror images, or as distinguished purely by whether the palm faces up or down. No single classical text settles it, and modern teachers inherit whichever convention their lineage used.
The distinction is worth holding onto because the second layer is the one most often collapsed into the third. A gesture named in a hatha or tantric text is attested there in a particular context, usually as one limb of a practice bound to breath, posture and attention. Lifting the hand position out of that context and attaching a health claim to it is what the modern therapeutic literature does, and it is a new claim rather than an old one, whatever the age of the name it travels under.