The latest clash occurred when Inverdale stopped Kiwi rower Drysdale after his historic gold medal win to get comment only for Redgrave to interrupt him and stop the interview, saying New Zealand TV needed to interview the single sculls Olympic champion first.
As Drysdale started to answer, Redgrave snapped and told the veteran British sports presenter to let him go and talk to the New Zealand broadcasters first.
Redgrave said: "I can't allow that to happen. The Kiwis should get him first. There's no doubt that's fair."
Later, when Drysdale returned to talk to the duo, Inverdale quipped: "Mahe Drysdale, the extended version of that interview."
The initial run-in occurred on Thursday, when Redgrave walked off and did not return for the rest of the day, according to The Sun newspaper.
That spat kicked off after Inverdale compared Redgrave to a mute James Bond character Oddjob to which the ex-Olympian said: "We'll have to call you Jaws because I can never get a word in edgeways."
As part of the ongoing tension between the pair, Redgrave also shook his umbrella onto Inverdale, covering him with droplets of rain. A source told The Sun: "Sir Steve was so livid that he walked off because he wasn't able to speak."
And those watching on their televisions at home, could not help but notice the simmering atmosphere between the pair.
Andrew Brooks tweeted: "And it's Day 6 in the When Will Steve Redgrave Thump John Inverdale competition."
Anya Grace added: "If the rowing doesn't end with Steve Redgrave chucking Inverdale in the lake I'm gonna be disappointed."
John Cadigan wrote: "Presumably Steve Redgrave is going to finish by belting John Inverdale into the lake with an oar."
- additional reporting The Telegraph