A picture of either your mats or the type of anchor you're referring to would be worth 1000 words.
If your mats are like the WeatherTechs pictured below...there is a "hook" floor anchor that can be used. The bottom of this type of anchor is like the typical BMW type (has a "T" (bayonet) on one side that gets inserted to a pre-cut slit in the carpet down the floor pan)...then there's a hook on the top side that protrudes up through a hole in the WeatherTech floor mat. This type of floor anchor uses the existing slits cut into the carpet and floor pan:
And I think I found the screw-in type that can create a new securing location in your carpet...only negative I see with these is that it creates another hole in the carpet if you have the existing pre-cut slits:
{this pic shows both types...the screw-in type (lower left) and the bayonet "T" type (upper center)}