I agree this is most likely a protein film. It is not dangerous in and of itself, but if it thickens (as it usually will with time and if not regularly dealt with) it will impede the gas exchange (oxygen in to the water, CO2 and nitrogen gas out) and this could harm fish and invertebrates in the tank.
I rarely see this, but in one tank for some reason it is present frequently though not permanently. It is often more prevalent in tanks with live plants (I know you said you have none, just pointing out the fact). Some filters can be fitted with a surface skimmer device, which can work to pull the water surface into the filter, thus removing the protein film with it. But in very small tanks the filter likely won't have this option, and it can get clogged with floating plants (and Betta should have floating plants).
When I see this in the one tank, at the weekly water change I simply invert the water changer under water so I can pull in the surface water slowly, and remove most if not all. It may rebuild by next week, but it is controllable. Some will suggest laying paper towels on the surface to pick this up, but I had no luck with that; the inverted water changer was more effective and easier.
Increasing the frequency and volume of water changes might help, and vacuum the substrate. Also keep the filter well rinsed. Organic buildup is part of this. Plant nutrients over dosed can contribute, but again you have no live plants so thee organics and nutrients are coming from elsewhere.
Byron.