Beckham, who is returning to the Los Angeles Galaxy, has been training with Spurs for the past six weeks to get fit for the start of the new Major League Soccer season in the United States.
The midfielder left Spurs after training on Monday, but not before ordering in pie and mash, a traditional working-class London meal. Redknapp teased reporters at the club's training ground when he said: "You don't know what it is.
"It's only us Cockneys that know - I had three actually; I nicked an extra pie. I was brought up on it in the East End, it was fantastic.
"He had them delivered but I think some of the foreign lads were not too sure what to make of it - so we had their portions!"
Redknapp had intended Beckham to play for Spurs on loan but the deal fell through last month. Redknapp, however, has since hinted Beckham could play for the Premier League club in future.
Tottenham travel to Blackpool for a league match on Tuesday and would climb to third place in the table, behind Manchester United and Arsenal, with a third successive away league win.
Redknapp is battling with a long injury list, which worsened on Sunday when forward Rafael van der Vaart was ruled out after aggravating a calf problem in training.
Redknapp thinks the Dutchman will be fit to face Wolverhampton Wanderers on March 6 and is confident he will be fit for the Champions League clash with AC Milan at White Hart Lane three days later.
Gareth Bale will also miss the game at Blackpool, as will Jonathan Woodgate, who picked up a groin injury in Milan last week on his first appearance for the club in 15 months.
Vedran Corluka, who suffered an ankle injury following a two-footed challenge from Mathieu Flamini at the San Siro, is another absentee, but Luka Modric is expected to play after showing no after-effects from his appendix operation.
