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Thanks for the picture. I take it that picture in not from yours it is from the web. Since it is dated from 2016
And I assume you live and operate your ride in the rust belt areas. (Your profile is lacking the location of city state)
So glad I moved away from SE Michigan.

So how about some information!!!
And don't know what transmission you have. Escape of that generation had 2 automatics and one stick. So, I have no idea what the cover is for.
What engine?
Hybrid or not?
Two wheel drive or AWD?

Is yours in similar condition?
Wonder how to remove something like that. It will come off when new. Corroded/rusted like the picture shows may require more effort.

Likely a cover from a donor vehicle in the Southern US areas would fix you up. And likely for low cost. Just need to know some info!
Before install I would coat the replacement. Paint, Clear or ??? Followed by wax.
I would also clean/treat the other parts in there as well. The rubber hose in the picture is NOT OE. It has been replaced as those are not factory clamps.
The rack boot could be treated too.

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If the cover is made of steel and NOT leaking there is a cheaper and crude repair.
Brush off the loose debris and paint with POR15.
All Products - POR-15 (por15.com)

Buy it at Amazon.
Follow the directions and/or coat the part a couple of times.

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Could not tell you about if there is a seal or gasket around the cover with out some data.

And don't know what transmission you have. Escape of that generation had 2 automatics and one stick. So, I have no idea what the cover is for.
What engine?
Hybrid or not?
Two wheel drive or AWD?

Likely what is behind the cover is a servo. If the transmission has a band that would not be accessible behind the cover.

If you use the POR15, do not remove the cover. Leave it in place.

The transmission case would be made of aluminum or an alloy. That material does not rust.
I assume the cover is made of steel as steel does rust.

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4 speed automatic or 6 speed?

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Interesting. Thought it was going to be the 6 speed.

That is a CD4E transaxle used in many Mazda and Ford vehicles from 1995 to 2008
I believe your part is a pump body shown below.
Part 510 in the 500 assembly.
No bands and no servo, it is the pump that generates the fluid pressure for the transmission to operate.
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Here is an Ebay seller selling at least 7 of them. These appear to be coated on the exterior
96500A - CD4E, PUMP WITH STATOR, 1997-UP, FORD, MAZDA & MERCURY | eBay

And a remanufactured one for less $. And this one looks like bare metal.
Remanufactured R96500A Transmission Pump (Retros 94-Up) CD4E 94-18 | eBay

You might be able to do more shopping and get favorable terms

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It would be a nice contribution to this site if you post pics of the job. Assuming you are going to do it.

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