Home Depot just responded to Tyrese's lawsuit ... pushing back against his claims of racial discrimination on the part of their cashiers.

According to new legal docs, obtained by TMZ, Home Depot claims Tyrese came into their store and brought a bunch of items to the cash register, where the cashier scanned everything. HD says Tyrese then went back for more shopping, leaving the register for 25 minutes and forcing the cashier to clear out his transaction.

It's a different story from Tyrese's original complaint, where he claims a computer glitch caused the delay. He also said that because of the alleged delay, people started recognizing him and, feeling uncomfortable, he went to the parking lot instead of staying around to oversee the transaction

Tyrese claimed he told the cashier his two helpers would finish the purchase with his credit card and said she understood his instructions before he left the store ... and said he was told he could go wait outside and she would finish the transaction.

Home Depot claims their surveillance shows Tyrese did NOT speak face-to-face with any of their cashiers.

Remember ... Tyrese also got on FaceTime with a cashier from outside the store and authorized her to complete the transaction his partners were trying to make with his card, but she -- and her manager -- said that wouldn't work, and he would have to come back to the store to show ID.

That's about the only part of the story both sides agree upon -- and, further, Home Depot says its surveillance footage shows Tyrese coming back into the store and getting into a heated discussion, which ends with him showing his ID and the cashier completing his transaction.

Tyrese told us it was hard to sue Home Depot because he's a longtime customer and the store is like his Disneyland ... but Home Depot says they don't know how long he's shopped there and aren't sure how much he's spent over the years -- Tyrese claims it's close to $10 million over 2 decades.