Simple operation on .txt files

I have a folder - like the attached one - containing multiple .txt files bearing names like, for instance,
BDX24Jan05Feb19Jan21Feb
As you can see from the attached, these .txt files contain rows of the form
BDX24Jan05Feb19Jan21Feb,20240102,252.65,265.11,252.61,265,71211
BDX24Jan05Feb19Jan21Feb,20240103,264.93,266.7,247.96,252.5,91344
etc, etc

All these names are fairly long, so what I want to accomplish is provide a string to the program (in our example here say the 24Jan05Feb string) and the program will CUT this from everywhere it sees this string i.e. now my text file names will be
BDXFeb19Jan21Feb
and its contents will now be like
BDX19Jan21Feb,20240102,252.65,265.11,252.61,265,71211
BDXFeb19Jan21Feb,20240103,264.93,266.7,247.96,252.5,91344
etc, etc

The program will do that for every .txt file in the folder I will provide to it, and even if this folder contains sub-folders, the program will do this for every sub-folder there.