There are many things you can try, and since probably very few of use have ever need to repair a screen and even fewer have ever seen that particular screen fabric I can not say. NOTE you have not told us if this is AT or solid fabric, my below comment would be for NON AT fabric made of PVC or some other no woven product. White gaffers tape is the type of tape I would use but before tape I would try latex see below
Here is what I would try first, get a small container of liquid latex at the hobby store the whiter the latex the better so open the lid and look in if there is more than one brand. Mold builder made by Castin'Craft is what i use and it does turn yellowis when dry.
Place the damaged section face down on a very smooth surface like a CLEAN glass or laminate table top.
Use some books or bags of new paper or something heavy to keep the fabric from moving but not crease or damage it.
Work the rip together as perfectly as you can use a magnifying glass if you need to.
Now using an artist brush or even just your finger, (practice on paper first) apply a thin coat of liquid latex over the rip without disturbing the surface.
Let it dry over night DO NOT TOUCH IT just walk away!
Laytex stays sticky even when dry, that is why latex cloves are powered.
Next day add another coat and let it dry 4 or 5 hours depending on temp an humidity add one more coat and walk away till then next day.
Dust the repair with baby powder and check the other side.. Since this is not glue it is reversible and can be pealed off and depending on the material not even stick but it is what I would try first. If the latex bleeds though the crack it is going to show up as more yellow than white.. but like I said it should be reversible and if you get the rip really tight it may not bleed through.
If this works really well and the comes loose, next I would try is silicone but there would be no reversing that.. I supose