Grizzlies are relatively new organisation to the league so there isn't deep history to bring up when we are looking at potential rivalries. Like it has been over 10 seasons already but it still doesn't compare well with some other teams that have multiple playoff or finals series versus same opponent.
So first thing coming to mind would be the Regina Elk, another team that joined at the same time for seasons 61. So far they have only met once in a playoffs during season 66 when Regina won in 5 games and there likely wont be another chapter to be added this season as currently Grizzlies sit 14 points out of playoffs after 18 games. Still neither team has really had success in form of a cup, with Great Falls being only one to even make it into the finals, back in seasons 63, so the race to the cup between these two expansion teams is still on which could be seen as form of a rivalry.