For other folks reading, be mindful that not all PC fans can efficiently draw airflow through a filter. The key word is “static pressure”, which refers to how much force can be exerted on a fully-blocked opening, which would then produce airflow through the parts that are less blocked. The simplest PC fans basically have zero static pressure, and so they’ll just spin uselessly when covered by an HVAC filter.

As an aside, dust and lint in PCs can be reduced by limiting dust and lint in the environment: replacing your home HVAC filter, not wearing shoes indoors, electrostatic fans, and using mechanical ventilation rather than opening the window are effective ways to keep detritus away from your machine in the first place.