The Premier League clash at Turf Moor was called off a little under an hour before kick-off due to heavy snow.
Ken and Brandi Saxton had spoke about their journey from Dallas, on social media: "In a message on Saturday, Ken Saxton posted a picture of the pair on the train with the caption: 'Dallas to London to Burnley (almost there) 31 hours - no sleep - fueled (sic) by coffee, cheese crackers and more coffee.
"Frigid temps and snow predicted for match day. The things we do when you love your club."
As the post picked up traction among Tottenham fans on social media, it was sent to Tottenham striker Kane who made a classy gesture towards the pair.
The England captain replied to their post: "Just been sent this tweet and absolutely gutted for you!
"vFor your commitment and to make up for the match being called off I'd like to invite you to a home game as my guest when you're next in London."
Kane's offer unsurprisingly went down well and Brandi Saxton responded on Twitter: "Well the husband has officially gone viral and we've personally been invited to watch the Spurs by Harry Kane!!"
Ken Saxton also replied to Kane: "Cheers Harry and not necessary at all, but we would enjoy taking you up on the offer. Thank you and to all Spurs (and other football fans) who have reached out. Amazing really."
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