I think this was the original post that set off my intrigue.Yes, I have attached some close-ups of photos from that blog post, as well as (sadly) some bags I see listed on a preloved website right now being sold.
You can see that there are lines in between the gaps where the panels are. The real Puzzle bags wouldn't have anything underneath the Puzzle panels (it should look like one solid piece underneath the top layer, if that makes sense). Absolutely none of the real Puzzle bags from Loewe itself will ever have these "separate" pieces - it should look cohesive and smooth in those narrow gaps.
Additionally, the Puzzle Edge bag from the blogpost has the worst stitching I've ever seen. That's definitely a fake bag. The stitches are white, whereas the bag should at the very least have tonal, or same color stitching.
That being said though, although these are only 2 way to tell the Puzzle bag is fake, I'm certain there are other fake bags out there that don't have these broken "seams" and have smooth stitching. Honestly, it all comes down to the leather feel and smell. For smooth calfskin, the fake bags will have a very slight "sheen" and look shinier, whereas the real ones will look more matte. The best way to authenticate a Puzzle/Loewe bag is to familiarize yourself with how the authentic Loewe bags' leather looks, smells, and feels. The fake bags will never be able to imitate the true, high quality leather that Loewe is known for, but it can definitely be deceptive to those who didn't know any better (such as myself), since replicas can still use leather, but at a much, much lower quality.
I was luckily able to return my fake bag. However, even though I submitted the certification from a 3rd party agreeing that the bag was fake, this particular reseller website where I bought it from, responded by saying that they "stand by their authentication process", said my bag was authentic, and re-listed it on their website. It has been sold to someone else. It's upsetting to me that the replicas are getting away with selling their bags online for the cost of real ones.
I hope this helps!!! Please, please do your research and be careful when buying Loewe bags online!
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Some other medium puzzles that are discontinuous in the back
https://www.therealreal.com/products/women/handbags/handle-bags/loewe-medium-puzzle-bag-ijiul (2014)
https://www.therealreal.com/products/women/handbags/handle-bags/loewe-medium-puzzle-bag-htbvx (2015)
https://www.therealreal.com/products/women/handbags/handle-bags/loewe-puzzle-bag-ifq0m (2016)
https://www.fashionphile.com/p/loewe-calfskin-medium-puzzle-bag-beige-597308 (2016)

LOEWE Calfskin Medium Puzzle Bag Black | FASHIONPHILE
This is an authentic LOEWE Calfskin Medium Puzzle Bag in Black. This elegant handbag is crafted of black calfskin leather. The bag features a rear zipper pocket, a black top handle, an optional shoulder strap, and silver hardware. This top zipper opens to a beige fabric interior with patch pockets.

LOEWE Calfskin Medium Puzzle Bag Tan | FASHIONPHILE
This is an authentic LOEWE Calfskin Medium Puzzle Bag in Tan. This stunning bag is crafted of smooth calfskin leather in light brown. The bag features a rolled leather handle, a rear zipper pocket, and an adjustable leather shoulder strap with polished silver hardware. The top zipper opens to a...

LOEWE Puzzle Medium Leather Shoulder Bag Red
Item Details: Designer: LOEWE Model: Puzzle Medium Retail: N/A Style: Shoulder Bag Material: Leather Color: Red Made: Spain Measurements: W 11" H 7" D 5" Accessories: No Accessories. Condition Detail: Excellent - The Item is in excellent condition with minimal signs of use. Outside: Signs of...

Loewe Handbags for Women - Vestiaire Collective
Buy second-hand Loewe Handbags for Women on Vestiaire Collective. Buy, sell, empty your wardrobe on our website.


Puzzle leather handbag Loewe White in Leather - 36818101
Achetez votre puzzle leather handbag Loewe sur Vestiaire Collective, le dépôt vente chic sur Internet. Puzzle leather handbag Loewe White in Leather à prix d'occasion. 36818101

Bonus, small on Fashionphile:

LOEWE Calfskin Small Puzzle Bag Kaolin | FASHIONPHILE
This is an authentic LOEWE Calfskin Small Puzzle Bag in Kaolin. This messenger bag is crafted of soft, supple calfskin leather in off-white. The bag features a rear zipper pocket, a rolled handle, and an adjustable leather shoulder strap with polished silver hardware. The top zipper opens to a...
Bags that don't have it
https://www.fashionphile.com/p/loewe-calfskin-medium-puzzle-bag-tan-1272220 (2017)
https://www.therealreal.com/products/women/handbags/handle-bags/loewe-medium-puzzle-bag-i4aw8 (2018)
https://www.therealreal.com/products/women/handbags/handle-bags/loewe-2021-medium-puzzle-bag-hva2k (2021)
Loewe Handbags for Women - Vestiaire Collective
Buy second-hand Loewe Handbags for Women on Vestiaire Collective. Buy, sell, empty your wardrobe on our website.

(2018)
https://www.selfridges.com/US/en/ca...multi-function-leather-bag_735-10143-32230S20 (selfridges)
My theory is that design maybe changed between 2016 and 2017? There's a lot of limited release bags that I'm seeing with this discontinuous pattern as well. I think I'll try to authenticate via legit grails!