Something in my house.... help

A few days back, when I got home my curtains were down on one window of my bedroom. I knew that my younger cat had done it. {The older one sleeps a LOT}. I figured she was chasing a gnat. She goes nuts over the littlest bug. That afternoon I was in a chair reading in my bedroom. My younger cat is on my bed and nightstand going nuts. She was on the bed, on the floor, jumping around like crazy. Again, I am thinking a gnat. I have seen her go crazy like that and usually when I get up to check on her, it has been a teeny tiny bug.

So, today I am reading the paper while sitting on my bed. I had thrown some of the paper on the floor by my bed. All of a sudden my little girl cat is going nuts around that pile of newspapers. I looked over to see the papers moving. Scared me. I thought it might be a snake. {you never know}.
I looked over to see a green Gecko about 6" long.

My cat would catch it, then it would get away. She did that a few times. I tried to get it with a plastic trash pail, but that did not work either.

A couple of days back I had gotten a baby Gecko out of the house {about 2" long}. Did not think much about it, until I saw the Mamma Gecko. They usually hatch 2 eggs at a time. Now I am wondering where the other baby is.

I read online that they can live maybe 2 weeks without food. It won't get much of the kind of food it needs in here.

The thing is, I don't want to be cleaning out my closet 2 years from now and find a mummified Gecko.

I also don't want that thing crawling on me at night.

Can I fix this situation? Or do I have to wait until they....... you know.