The best way to do it right would be a fan and filter in the tent extracting out through ducting and out of a window or out through a chimney or into another room where the heat wont come back, pushing it out into the room will make the room hot and the tent will eventually be drawing hot air back in.
If space in the tent is an issue then filter in tent and fan outside works just the same.
You can run a filter in the tent and another in the room itself which would just scrub the air and spew it back into the room. That would certainly keep the house smell free.
Don't use cheap filters!