But they were at least able to sign a familiar replacement, in Josh March.
The 26-year-old returns for a second spell at Wetherby Road after joining from Stevenage for an undisclosed fee.
March scored five goals for the club while on loan from Forest Green Rovers in 2020-21.
“We are delighted to have Marchy back with us,” said manager Simon Weaver. “He plays the game with lots of energy but also knows where the back of the net is. In his last spell with the club he scored freely and anytime he crossed that line you knew he was going to be a threat going forward.
“He has an edge and that’s what we like about him. Obviously, since he was last with us, he has had promotion experience with Stevenage and Forest Green. Having those experiences brings an understanding of what it takes to do well at this level.”
March added: “I have nothing but fond memories of my first spell and I know the gaffer and Thirs (assistant manager Paul Thirlwell) well.
"As soon as I heard of the interest I was keen to get it over the line. I feel like I have unfinished business here.”
His arrival keeps good on Weaver’s promise not to sell Armstrong without being able to land a replacement.
Once Hollywood-owned Wrexham met the Sulphurites' valuation, the son of former Middlesbrough striker Alun was allowed to move on.
"We have reluctantly decided that Luke can go to another club," said Weaver.
“It has taken its time because we wanted to keep him, he’s been a great player for the club and we wanted to look after the club and get a good fee in and we’ve managed to do that, but we wish him well.
“He’s been fantastic and I’m glad for him that he’s got back to enjoying his football at Harrogate Town, in some ways it’s a feather in our cap that a player has enjoyed it so much and felt freed up.
“I think it’s a winning situation for him and for the club because we’ve got a really good fee.
“When a player says I want to go and my heart is elsewhere then you have to take it seriously and consider the affect it might have on the team and himself should it not go his way, so in the background we have been working really hard on bringing in centre forwards.”
Armstrong scored 31 goals in 106 appearances at the club, and was top-scorer in both his full seasons at Wetherby Road.