The Arsenal legend is working as a pundit for ITV at the World Cup, with popular presenter Woods hosting plenty of the action.
In a column for the Telegraph, Lynam bafflingly criticised Woods for calling the 59-year-old "Wrighty" while working on the Netherlands' 2-0 win over Senegal.
He wrote: "This was the first live match for ITV and was presented by the ever–smiling Laura Woods.
"She has done quite a lot of presentation work on both radio and television and comes over as both confident and capable.
"She called Ian Wright ‘Wrighty’ which sounds comfortable coming from the likes of Lineker but it made me slightly wince.
"I may be wrong and perhaps they are close friends but the over-familiarity made me a touch uncomfortable.
"The other pundits were Gary Neville and the former Dutch international Nigel de Jong. Laura refrained from calling them Gaz or Nige."
Responding to Lynam's dig, Woods wrote on Twitter: "Jeez. Of all the things covered this is what made Des wince?"
Wright also took to social media in response to the column, adding: "How’s Des vexed that Laura called me ‘Wrighty’!!! Looking for something negative to write."
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While appearing again with Woods during France's 2-1 win over Denmark, Wright made another brilliant dig at Lynam.
Woods had asked him: "Is that another example, Ian, of where some people aren't impressed by it?"
To which he responded: "You know what Lozza, it doesn't matter, you don't have to call me Ian.
"Look, how long we've known each other? Call me Wrighty like you normally do."
A second tweeted: "As a Spurs fan I couldn’t stand Ian Wright the player. As a pundit and person I think he’s brilliant."
Another added: "He’s a national treasure."
