The left-back has been training with the Jags in recent days and was given the first 45 minutes of the 1-1 draw with Dumbarton last weekend as he looks to win a deal at Firhill after his release from Plymouth Argyle.
He was the only trialist on show in Belfast as both of Archibald's summer signings - Ryan Stevenson and Abdul Osman - were handed starts against the Glens.
Archibald remains in the market for more reinforcements ahead of the big kick-off, with a replacement for Aaron Taylor-Sinclair at full-back one of his top priorities as he also targets a centre-half and striker to bolster his ranks.
Former Crystal Palace kid Parsons was given a another chance to impress at The Oval as Thistle recorded a 3-1 win, with Kris Doolan, Gary Fraser and Kallum Higginbotham on target.
Doolan opened the scoring for the Jags midway through the first half before Glentoran equalised from the spot after a handball from defender Jordan McMillan.
Fraser put Thistle ahead late on with a deflected effort from range before Higgin-botham added his name to the scoresheet with a cool penalty.
Thistle will continue their preparations for the new Premiership campaign with a behind-closed-doors clash against Rangers tomorrow before they head south to face Fleetwood Town on Saturday.
The Jags will then host a Sunderland XI at Firhill before they kick-off their second term in Scotland's top flight at home to Ross County on August 13.