Chester had previously expressed an interest in Lowe but their method of approach angered Town.
Peters told ShrewsWeb: "Since he's had wind that Chester were interested in him the only good game he's had was against Chester.
"He hasn't really had his head in the right place he's been more unsettled by the move and wanted to go."
As for Grant, he has not featured much this season, and the chance of first team action was too good to miss. Peters was full of praise for the former Telford man: "He's not been getting in the side so it's a good move for him to go to Halifax", he told the official site, "John's a great lad who runs and works very hard for the team and I can't fault him on any of that."
The news comes on the heels of the capture of young defender Gavin Cowan. Peters clearly rates the 23-year-old and was persuaded to fork out £5,000, which rises to £15,000 on appearances.
Peters also said there would now be no more squad changes until the club were safe from relegation.