Can you give us the model and spec number of the engine? I am curious about the existence of a filter too.

Sorry about that. Engine 143.955500 carb 632681

My drawing says primer filter #632647

I think these are the little foam pucks you sometimes see. I wouldn't lose sleep over finding one...

I opted not to put one in. The foam filters that I saw that I could cut and insert in there made me nervous. They seem like the kind of foam that deteriorates after a few years and starts to break apart. I was concerned that I would just be injecting foam parts into the bowl. I'll take my chances with outside dirt that will probably settle to the bottom of the bowl anyway.

These foam filters are made out of foam that will not deteriorate. This is used in many differnt applications. Brake caliper manufacturers use different density foam to control brake pedal rate of return. It controls the flow of brake fluid through the caliper. Higher density foam slows the speed of fluid therefore slowing the pedal return rate. Too fast makes a noisy pedal that customers dislike kind of like if you sidestep the pedal near the top. Too slow makes a dangerous brake pedal as you may need to reapply the brake in an emergency. In a mower this will control fuel flow when the carb lacks adjustments. It will allow the fuel to go slower and mower will run better than if it were absent normally. It is really a cheap to make up for poor designs by engineers that don't have the time or money to actually correct a problem. It is by some companies now a standard practice.