I can't imagine a tenant having to go to a DIY store to purchase an air filter for your furnace. You can get them for less than $5 and leave a dozen of them on the side of the furnace. I don't even ask our tenants to change the filters since sometimes getting the metal pieces of the furnace back together takes a little mechanical talent and when the filter is inside the furnace there are a few bad things that occur e.g. if the door is not properly closed the safety switch will be open and the furnace will not operate and you get to pay a technician to solve the problem and tenants sometimes don't installs filters correctly and the filters get sucked up into the blower squirrel cage.
Don't forget to check/change the filter if you're ever there for an inspection. Provided a years worth of filters to my tenants, found the same ones still in the laundry room when they moved out. Lesson learned.
My tenants are lazy and don’t change the filters. I drop a half dozen of them off occasionally and ask them if they need more. Some of mine are too lazy and cheap to change the smoke detector batteries. I’ve gone over to a couple rentals lately and they were beeping due to battery low. I asked them how long they’ve been doing that annoying chirp. They said a few days.