Leave the stickers on and purchase a box or boxes to store the slabs in. They will help protect the lenses from scratches and as @masterswimmer suggested the stickers will serve as a filing identifier/ cross reference to your spreadsheet (assuming you have a list).
Even still, that is a solid image that can be used for coin identification. the staff has been playing with a Free AI system https://www.tensorflow.org/install/ and standardized images like this would be wonderful to train the system.
Just remove the stickers. You can positively tie the coin to the auction via the slab's certification number (and also from the Heritage paperwork you received with the coins).
I have a folder where I document my purchases and I usually peel the sticker off the slab and stick it to the page next to the entry, along with the date and the price I paid for the coin. Pretty much the only auction houses that I buy from that have stickers are Heritage and Great Collections.
The stickers become difficult to remove later. I remove all of them and stick them to a piece of paper. I find those that were left on leave a residue behind (and become difficult to remove). Some mess with the hologram on the slab.
One, you can keep the HA numbers (to the coins) without them being on the slabs...save whatever paperwork you receive with the corresponding numbers to coins...surely they provide something of that sort...if prices are present then copy the info and custom cut or cross them out for when/if you don't want to share them...and finally, you can just create your own file with the info as you want it and save it. Two, if the adhesive is heavy and sticky...like old or brand-X tape...take them off soon(er) and be done with them...you'll be glad you did in the long run as that stuff tends to slowly "run/melt/spread" over time and conditions, and then it's a real pain.
I have never seen a good reason to leave the auction house stickers on the slab and a couple of good reasons to remove them. My reasons for leaving stickers on - None. My reasons for removing stickers - Adhesive issues; blocking slab hologram; not suitable for ID'ing because nothing guarantees that duplicate lot numbers won't appear; and finally, I hate providing free advertising on what I own be it cars, shirts or coins. I do, however, always record in my database the auction house, date of auction, auction number, lot number, hammer price, BP, S&H, ancillary costs, slab certification number, die marriage, rarity and any other information that I think can or might be needed for any of the potential uses of the data. This written data complements all the photographic recordings I make which consists of the auction house photos, my photos of slab and close-ups plus photos used in die variety identification and die state markers.
I'd remove them in a heart beat. They can easily be copied or removed to be put on other slabs, so lend no authenticity to the coin.
To show "provenance" to the HA Auction, you can take a photo of the slab with the sticker showing, and also with the cert #, but I would suggest that you remove the sticker as I've found from experience that the longer a sticker has been on the slab the more difficult it is to remove in the future, especially those stickers that have been placed on the reverse that cover the Foil Hologram where removing it frequently damages the foil. If you do have one that has adhesive residue on it, you can remove the residue by using a Q-tip saturated with Orange Oil (D-Limonene) Cleaner and apply the liquid to the adhesive area and gently agitate the Q-tip until the residue softens to the point that you can remove it with another wet Q-tip; after removing the residue use another dry Q-tip to absorb the diluted residue until only a slight film remains, then use a Q-tip or soft cotton cloth wet with warm water to remove the film, and again follow up with a dry cotton cloth. If you follow this procedure you will remove the adhesive residue without leaving scratches on the slab.
If you leave the sticker on to long the glue can be hard to get off the slab. I found that if I take them off when I get them it's no problem. If you want to keep them as a way to keep track of them then that's fine as long as you know that a year or two later you may have a hell of a time to get the glue off.
But I mean worst case scenario the slab ends up with some sticker glue residue on it right? That wouldn't decrease the value of a coin would it? Since slabs can be sent in and re-slabbed.
Yes take off the suction stickers, they need to go. I would not want that crud on my slabs. I remove them as soon as get from AUC House.
I agree with some of the reasons to remove the stickers, but the main reason I leave them on my coins is to know quickly which coins I've purchased from Great Collections or HA. If I chose to sell them on eBay, I go to GC or HA and use their photos for my listing. That saves me considerable time when listing coins on eBay. However for a coin that I think I'll hold for a long time, I agree with the reasons to remove the stickers. Goo Gone gets off all the nasty adhesive residue if you have to resort to that.
if they cover any of the labels i remove them... the longer they are on the harder they are to remove cleanly... the only 3rd party stickers i tolerate are CAC and the pcgs/varslab label (which does cover the pcgs rear label)
Nah it would just be the Heritage Auctions and WINGs stickers not the CAC green beans and gold beans. xD
Fast forward 50 years, let's say heritage is gone. Now some lucky guy has all these slabs with these old auction house stickers still stuck on them. From an online auction place that is no more... you just never know. That might be like a cac sticker is now. It might add value for no other reason than it is an original sticker. That's just my thoughts. Once removed it's gone forever. Regardless of what you do i would have every slab in a small ziploc. If you use the pcgs storage boxes it's not a big deal. But if you don't I would ziploc everything. When I take my pcgs coins from the box they go right into ziploc.