John Steed wearing a Bow Tie
The Grandeur that was Rome
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Series 3:
Concerto, The Grandeur That Was Rome, The Undertakers, Esprit De Corps
The Grandeur that was Rome
dark navy bow tie with white dots
Wearing a Tuxedo with a black bow tie in Concerto
Dark navy bow tie in The Undertakers
Wearing a Tuxedo and a small black bow tie in Esprit de Corps
Series 1:
The Frighteners, The Yellow Needle
Tuxedo with small black bow tie in The Frighteners

T
here are photos of Steed wearing a bow tie in The Yellow Needle in Leonard Whites' scrapbook
Series 2:
Death on the Rocks - Tuxedo with dark small bow tie
Series 4:

Dial a Deadly Number, Room Without a View, Quick-Quick Slow Death, Honey For the Prince
Tuxedo with black bow tie in Dial a Deadly Number (left), Room Without a View and Honey for the Prince (right)
Black tie on waiters uniform in Room Without a View
White bow tie with tailcoat in Quick-Quick Slow Death
Series 5:

The Fear Merchants, From Venus With Love, The See-Through Man, Never, Never Say Die, Return of the Cybernauts, Death's Door, Dead Man's Treasure, £50000 Breakfast, Murdersville
The Fear Merchants
From Venus With Love
The See-Through Man
Steed adjusting his bow tie in Death Door
Return of the Cybernauts
Murdersville
Series 6:

Get-A-Way! , Look - (stop me if you've heard this one) But There WereThese Two Fellers..., All Done with Mirrors, False Witness, Noon Doomsday Legacy of Death,  The Morning After, Who Was That Man I Saw You With?, Take-Over, Bizarre
Get-A-Way! , Look - (stop me if you've heard this one) But There WereThese Two Fellers..., All Done with Mirrors, False Witness, 
The Morning After                                         Noon Doomsday                                               Who Was That Man I Saw You With?
A last good look at his purple tuxedo in Bizarre
Steed with untied bow tie in Take-Over
TNA episodes with Steed wearing a dark green tuxedo and a dark green bow tie are:

The Midas Touch, House of Cards, The Last of the Cybernauts...?, Three Handed Game, Hostage, Trap, Dead Men are Dangerous, The Lion and the Unicorn, K Is For Kill - Tiger By the Tail (2), Complex
House of Cards, Hostage and Dead Men are Dangerous