After having a new HVAC Carrier system install in January, Munn's told me the same thing, hot water once a month.

No chemicals

Great idea! Also pouring hot water down the condensation drain helps prevent gummy buildup. Should do that once every couple of months.

. Our original one (2009) was installed by the Villages Builders (actually by SUN-KOOL) as well and it did have the trap out in the back yard next to the condensing unit. Shows how T.V. builders lack consistency, or maybe your original just got removed or broken. In any case, the manual from our 3 month old Carrier system says that CARRIER requires one and if it is like here as in that article from VA I linked **IF** local code says one is only needed **IF** A/C manufacturer requires it then those without one are in violation of code (not that it means a hill of beans just a POI). That article was about VA and I didn't look through code here as it really wasn't of importance, just a DP.

My neighborhood was built about 7 years ago. All of the houses have a Carrier HVAC system installed by Munn's. To my knowledge, none of them have a P-trap on the condensate drain line, either near the inside air handling unit or anywhere outside the house.

“ Current IRC and Florida code (M1411. 3) does not require a p-trap in the condensate drain line.Sep 25, 2021”

Flushing out condensate line with hot water and a drop of dish soap is the safer way to go. Once a month minimum.

To answer the original poster's question...
The screens in the picture are commonly installed on gas furnace air lines to prevent things from crawling into the pipes. They are not used on the condensate drain line. These pipes are air for combustion, and the exhaust. Currently, air pipes are 4" dia, but these look to be older, a smaller diameter.

DO NOT follow advice here to put in a P-trap, or flush these AIR LINES with anything.

The screens pictured are good because they have a much larger total surface area than the pipe cross section. Better screens will have openings in the screen that are a bit smaller, and larger overall screen surface area to reduce the pressure restriction that comes with adding a screen. These screens have a large volume of air moving through them.

Condensate lines are usually 3/4" or 1" diameter. If you can find a screen that diameter, and put it on condensate line, it may prevent some things from getting in. A gecko can squeeze thorough a very tiny opening. If you make a screen with tiny holes the size of window screens, it would likely plug up. I would not stretch a window screen across the opening of the PVC - that's asking for problems.
Any screen you add must be stainless steel.
Might want to look into this
hXXps://pvcventscreens.com/product/svc-is075/
https://pvcventscreens.com/product/svc-is075/

If you are flushing the condensate line regularly and correctly, it is highly unlikely that an anole or any insect will be able to clog up the drain. A snake? Maybe. I have never used a screen on a condensate drain, and have never had a clogged condensate drain. So, I don't plan to do anything to correct a problem that doesn't exist. Clogged condensate drains are an issue that can shut down your HVAC system, but the usual cause is improper maintenance.

Note that the drain pan located under the evaporator coil has an electronic float switch that will shut off your HVAC system and prevent any water damage. I don't pay for regular HVAC maintenance, but if you do, I would suggest that you require the technician to test the float switch for proper operation.

After what Munn's told me to use hot water and reading the problems that a
screen can cause, or until I have a critter problem, I think I will just do my monthly maintenance.