I'm dealing with this right now.
In my area NO tire stores that I could find buy tires back, even brand new ones like we have. I actually have six practically new stock sized tires. Four GY Integrities like you have and two Bridgestones that were/are spares on our XL7 and our previous GV. The Bridgestones have no mileage on them and the GY's have maybe 200 miles on them as I put better tires on ASAP.
The local paper lets you run ads in the "under $100" category for free if you place them online. Well, I've been doing that for about a month now and have had plenty of calls but no takers. I've got them listed for $50 each and won't go lower since they're practically new and the local Goodyear place wants $90 each for the same tires.
Also be prepared for the people that don't know jack$hit about tire sizes other than their car has tires that have 235, 60, 16, some combination of some of those numbers, one of those numbers, or just tires on it. I had a guy all ready to buy the first week...I pull up and realize he's driving a F150.
"Those are kinda small."
No $hit moron...I even have the complete tire size in the ad too, he didn't know what size tire his F150 ran...235/70R16.
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Some old guy wants to come see them, but can only come by during the day on weekdays...while I'm at work..."no, I won't let you randomly sift through my garage while I'm not at home sir."
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Then there's the , "I'll call back on Saturday..." calls...so far I still have them.
Have fun...luckily I have a storage shed and they're not in the way...cause they sure aren't moving right now...
They might end up on Ebay for stupid cheap soon.