Go and buy another TV, use a credit card. Return it saying you've lost the receipt but take your CC statement. All above board. You should get a refund.
You now have a receipt. Feel no remorse, but know you're a scumbag.
But then he's still left with a tv?
I'm assuming he doesn't need a tv, as opposed to just not wanting that one.
The only way your suggestion would make sense is if he wanted another tv at £299 that tesco sell that isn't in the offer, he could buy the tv he did want, use the statement as "proof" of a £299 purchase and then return the lg.
I.e he wants a £299 Sony but tesco doesn't have the Xbox offer on that particular model, so he buys the Sony. Then buys the lg Xbox bundle, but uses the credit card statement used to buy the Sony to return the lg.
But he seems to just want a cheap Xbox as opposed to not liking the lg to and wanting an alternative.
Your suggestion doesn't get him any money back, just simply switches the tv for a different one.
Anyway all suggestions are technically fraud, and for what in a supermarket is a "High value" item, you will simply not get a cash refund with no proof of purchase.
It's one thing maybe going in there with an item of clothing with no receipt and swapping it, or possibly cash refund (which is extremely rare with no proof of purchase) but a 300 quid item?!
Best thing to do is just be blatant, buy the bundle, then go instore with receipt and try it on. Worst case they say no, and you go with your eBay plan. Best case is you get someone a bit thick who doesn't realise and simply refunds the tv.