Most owners won't have the packaging. That's fine. The identifier you need is on the warmer itself.
HotHands: model H163650 on the underside
Health Canada says the HotHands model and batch numbers are printed on the underside of the warmer, with the white HotHands logo on top. The recalled units are white with orange, sold in packs of two that join magnetically, with a USB-C charging port, adjustable heat, LED indicators and a silicone lanyard. If the underside reads H163650, it's covered. Note the batch number as well, because the refund claim asks for it.
This recall covers only the rechargeable model. Disposable air-activated HotHands packets aren't part of it.
Gobi Heat: UT3053 on the underside
The Canadian notice lists the Gobi pair by SKU and UPC but doesn't say where on the warmer the number is printed. The U.S. Consumer Product Safety Commission's Gobi Heat notice answers that: "Gobi Heat" is printed on top of the warmer and model number UT3053 on the underside. The warmers are black with grey accents, sold in magnetically joined pairs with a charging cable, LED indicator lights and a silicone lanyard.
Why UT3053 alone isn't enough
This is the detail that connects the October recalls to the September one. Health Canada names Shenzhen Street Cat Technology Co., Ltd. as the Gobi warmer's manufacturer. The same company appears as the importer, doing business as OCOOPA Direct, in the OCOOPA recall. UT3053 is also one of the seven OCOOPA models recalled in September, and OCOOPA's own recall page lists it as the UT3 Lite.
None of the notices says the two products are identical, so don't read more into it than that. The practical point is narrower: a warmer stamped UT3053 on the underside could fall under either recall, and the brand printed on top decides which one. A Gobi Heat logo means you contact Gobi Heat. An OCOOPA warmer means the September recall, RA-82578, which also covers models UT3056, ZLS-118, ZLS-118S, ZLS-118D, H01 and H01(PD).
Photograph the underside label and the top logo before you do anything else. Both refund processes ask for photos, and having them on your phone means you only handle the warmer once.