engine oil mesh leak

do you mean it leaked from where the plastic seemingly contacting the transmission cast?
there's a rubber seal inside and you gotta lose some oil although if you can cork it with something quickly after removing the mesh , u'll lose maybe just a quart.

 

Yes/and no on removing oil...

My last oil change, I managed to crack one of the "ears" on the oil suction fan. It caused a slight drip. You might want to check if that is what you did too.

Once my new filter arrived (in stock at Ricambi), I jacked only the passenger side (maybe 8" which gave me enough comfortable room to work), placed a NEW oil catch pan under the suction fan, used painters tape and aluminum foil to create a dam/route for oil to go straight to catch pan, then removed/replaced suction mesh fan/filter, being careful NOT to over torque. Then the oil that did come out, I measured, which was not much as I recall...maybe less than 1/3 of a qt since I had the car jacked at an angle, then put that clean oil back into the oil fill. I did this all with the car COLD so the oil would not flow as quickly.

~$290 mistake, but worked out in the end, and a lesson well learned.
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You can as above remove it and pull it out. I have always done it with no oil in the car so can't comment on its feasibility.

You could also hypothetically put a metal plate with two holes that match the holes above on top of the plastic.. and then put on the two 10mm nuts that hold it into place with the metal plate ontop of the plastic like one big washer. This is if the plastic is cracked as above. It would in theory replace the pressure on the plastic that was lost with the compromise of the plastic above. Then order a new fan and install it.

If its the O-ring which it could very well be.. then you're SOL. Order both the O-rings from ricambi and re-install them. Oil is cheap.