I dunno if IDF has said anything about this carpet issue explicitly, but they are fighting a war, not conducting crime scene investigations. So expecting them to tag, bag, and photo every weapon where it's found is a bit unreasonable.
They actually tried to do something resembling that on one occasion, at al-Shifa, but soldiers are not crime scene investigators by training and there was then even a wee bit of controversy surrounding the placement of one extra gun in various footage taken at different times in one MRI room.
Yeah, if you read some US army manual on "Site Exploitation" (ATP 3-90.15), they suggest doing it more like a crime scene...
The photographer turns slightly, standing in place, while taking a photograph after each slight turn until the entire area or room is photographed.
But one has to wonder how often the US army did that in practice. (If you want to see something resembling this, there's e.g. a 2007 collection of 35 images by the US 1st Cavalry Division from a Mosul IED workshop --somewhat incorrectly labelled just a "weapons cache" in the source; I'm not pasting them here as there's too many photos.)
That manual also suggests though that when handling evidence:
The collected items are arranged at a collection point and photographed or videotaped together.
[...] The chain of custody documents remain with the items at each transfer point.
The IDF perhaps has a manual equivalent to that, but I dunno where to look for it. Anyhow, the IDF relies more on conscripts whose training probably prioritizes essential combat skills more than these ancillary aspects, but probably some IDF intel units specialize in this too.
Australian army tarp with probably Taliban weapons cache:
An Australian soldier catalogues a portion of the enemy munitions recovered during an operation in the Uruzgan province of Afghanistan Nov. 14 [2010].
That's also done even by the Myanmar rebels (allegedly that's materiel captured from the army):
(There's also older video on reddit of them doing that after reportedly capturing an army base, with the cheesy "a few moments later" thrown in.--NSFW warning: this footage also shows dead bodies.)
Or an YPG presser showing material said to have been captured from ISIS etc.