A/T Filter (pic) Is this it?

Specs: '01 Tacoma DoubleCab 4x4 V6 4spd Auto (19 bolt pan).
Truck has 70K miles and not sure if the trans fluid has been changed. Bought it w/ 45K from dealership, but I guess that doesn't mean they've serviced it before.
My auto trans has been acting up and I'm in the process of doing a drain and refill a couple times (doing the 2nd drain/fill tomorrow) to get the old fluid out and then drop the tranny pan and change/clean the filter. The old fluid I got out was pretty dirty looking and not very red anymore. I've read on several threads that it's just a screen that you clean and reinstall, but I went to several parts stores and they show this A/Trans Filter Kit:

There is a "screen" inside this filter, but it's a sealed unit with no way to take it out and clean it. Is this what mine will look like (haven't dropped the pan before)? If so, why does everyone say to clean it and not replace it? This kit is less than $30.
I'm just hoping this will fix my shifting problem. It started shifting hard while engaging 4th. 1st-3rd shift smooth. The shift lever also started to bind up a little after I did the first drain/fill, but doesn't do it all the time. Not sure what that's all about?!?
Thanks ahead of time for any advice you may be able to give.