The reason you haven't received a reply to your question is simply that you posted during the 3 hour period we set aside every day for silent meditation and self awareness.
Here's how the plumbing drain pipes in a typical house are connected:
1. Inside the wall beside or behind your toilet is a vertical pipe that runs from just below the basement floor concrete to just above the roof shingles where it's open to the atmosphere. Typically, most of the drains in your house will discharge into this vertical pipe, as will the toilet near it. That pipe is commonly called "the vent stack".
2. Coming off the bottom of the vent stack (under the concrete basement floor will be another pipe that connects the bottom of the vent stack with either your septic tank or the sewer buried 16 feet down under the middle of the street your house is on. That pipe won't be horizontal, but will slope at a shallow downward angle from the bottom of the vent stack to the septic tank or the sewer. THAT pipe is called the "main drain line".
3. Buried around the perimeter of your house's foundation, and at the base of that foundation (called "the footing") will be perforated pipes which allow any ground water around you're house's foundation to drain away (thereby greatly reducing the hydrostatic pressure causing that water to penetrate through your basement walls. These perforated pipes are called the "weeping tiles".
4. Depending on where you live and what your local plumbing code says, the weeping tiles will drain into either a sump pit in your basement floor or into the sides of a floor drain in your basement floor.
5. If you have a sump pit, there will be a pump that pumps the ground water that collects in that pit out. Where it pumps it (into a drain or onto your property somewhere depends on your local plumbing code.
6. If you have a floor drain (aka: "catch basin") instead of a sump pit, then there will be a p-trap at the bottom of that catch basin. Another pipe buried under your concrete basement floor will connect that p-trap to the "main drain line" from your house.
7. Typically, in newer houses, the laundry facilities located in the basement will drain into the catch basin instead of the vent stack. The reason why is that during periods of no rain, it's possible for the p-trap at the bottom of the catch basin to dry out, allowing sewer gas to come into your house from the main drain line. By connecting the washer and the laundry tub drains to the catch basin, you refill that p-trap every time you do laundry.
OK, so the question was, why isn't there a screen at the top of the vent stack?
And the answer is: Because the vent stack is a vertical pipe, so anything that goes into it will fall to the bottom. And, whenever the toilet flushes or the dish washer pumps water out, then anything at the bottom of the vent stack will be carried by the draining water into either your septic tank of the city sewer system.
And, varmints also have enough sense not to intentionally go into a vertical pipe which they know they won't be able to crawl out of. (There is the remote possibility of a goose in flight having a heart attack and plunging like a cork into the top of your vent stack, but until now, such occurances haven't been enough of a problem to warrant remedial action.)
But, just as you don't really need a screen at the top of your vent stack, there is no reason not to have one, as long as you ensure that that screen doesn't become clogged, thereby effectively plugging the vent stack and preventing your vent piping from operating properly.
So, if you have a screen over your vent stack, leave it there, but check it periodically to make sure that screen isn't clogged or anything. You need air to be able to flow into the top of that vent stack, and for sewer gas to be able to flow out the top of that vent stack. But, a screen there won't do you any harm. It won't do a whole lot of good, but it won't do any harm...
...unless it gets clogged up with snow, or the warm moist air coming out of that vent stack melts the snow and causes an ice cap on top of your vent stack.
If it were me, I'd be concerned that that screen could do more harm than good in the winter. But in the summer it shouldn't cause a problem.