As Mauro says TMTires.MAS is base ISI content, I can't remember offhand which ISI update fixed the F2/3 skidsounds as I use my own fix. You need the ISI TMTires.MAS and its MFT file.
It might just be the heat affecting me here in the UK but those 3 pics all seem to be the same! Though I do notice there seems to be 2 instances of TMTires, do you have 2 folders inside TMTires say 1.0c and 1.0c (1)? If so might be able to delete the non ISI one and see if that helps, the ISI file is 16.5MB (in explorer) and dated 7th March. Short of someone posting the MAS and MFT files it might be quicker in the long run to just make another install.
The problem seems to come because the 'fix' replaced the default ISI file which isn't a good idea. At the time I'd heard there was a fix but I couldn't be bothered to sign up to their forum to get it so I did my own fix. I can't complain too much because I did it the same way they had. I did notice that in the Advanced tab in the launcher that it 'had failed to verify, removed from inventory' and guessed that might cause problems later on but it worked and I wanted to get racing, I could fix it better at a later date.