The P3 canteen covers were introduced in 1943 from experiences in the Pacific theatre. They are made from cotton canvas like other US webbing of the period, but have long cross flaps to better secure the canteen. The hole at the bottom of some examples was to allow the covers to be used as a funnel to minimize water waste (source: https://www.usmilitariaforum.com/forums/index.php?/topic/224585-which-usmc-canteen-was-first/&tab=comments#comment-1779386). Some canteens were manufactured without the hole and used that way, though many were modified in the field or at a depot.

Sample 1: No Drain Hole
Appears to be entirely unused.
Sides:
Bottom:

No drain hole.
Top:

Open Flaps:

Inside:

Unlike the Army canteen covers, these were not lined.
Sample 2:
Issued and used. Has drain hole at bottom to be used as a funnel.

Sides:
Bottom:

Open Flaps:

Name written and stamped on outside and under left ear. The red mark’s meaning is unknown as of 7/28/2021.
Inside:

Usage Photos:
P3 canteen covers were used occasionally from 1943 through the end of WW2 (1945) (source: https://www.usmilitariaforum.com/forums/index.php?/topic/181721-wwii-p3-canteen-covers-opinions/&tab=comments#comment-1398733), and later in Korea (1950 – 1953) (source: https://www.gear-illustration.com/2016/03/06/marine-cross-flap-canteen-cover/, pictures below in Korea section).
Peleliu (September 1944):
September 15, 1944: D-day Peleliu, African Americans of one of the two segregated units that supported the 7th Marines – the 16th Marine Field Depot or the 17th Naval Construction Battalion Special take a break in the 115 degree heat (from https://commons.wikimedia.org/wiki/File:%22Peleliu_Island…Marines_move_through_the_trenches_on_the_beach_during_the_battle.%22,09-15-1944–NARA-_532535.jpg, https://catalog.archives.gov/id/532535). Marines of the 1st Marine Division firing an M1919A4 .30-caliber machine gun during the battle [of Peleliu]. From the Frederick R. Findtner Collection (COLL/3890), Marine Corps Archives & Special Collections OFFICIAL USMC PHOTOGRAPH. (Photo from https://m.k.sohu.com/d/450934823?channelId=1&page=1, Caption from https://www.americanrifleman.org/content/the-battle-of-peleliu-and-its-relics/)
Iwo Jima (February – March 1945):

Korean War (June 1950 – July 1953):
From https://bemil.chosun.com/nbrd/gallery/view.html?b_bbs_id=10044&num=125644. On backpack of marine on far left (from https://bemil.chosun.com/nbrd/gallery/view.html?b_bbs_id=10044&num=125644)? American Marines advancing after landing at Incheon, South Korea, in 1950. Credit: Bert Hardy/Picture Post, via Getty Images (from https://www.nytimes.com/2018/04/25/world/asia/korean-war-.html).