This is a translated version of the workaround from russian Maemo/MeeGo/Sailfish community on 4pda:
1. Go /home/user/.cache/data/twitter/profile and find a folder named as the first two letters of your twi login (example: for twitter login KoltyshevNV it's a folder named Ko, so it's case sensitive).
2. There are files named like $LOGIN_bigger.png and $LOGIN_orig.png (where $LOGIN means your login). The file you want is $LOGIN_bigger.png, delete it (you can simply check it by opening).
3. After that you should play around with standard twi app (I opened my twitter profile in the stock app, then clicked on my avatar to see the original, whereas 4pda advises just to post anything). You will see you normal avatar in the app.
4. This is VERY IMPORTANT! If you ignore this step, your avatar will break again some day, so to prevent it you should do the following in terminal:
where YOUR-FOLDER is a folder you've found in the first step of this instruction and $LOGIN is the same as in the second step.

Since this moment your twi avatar on the feed page will be normall (note that your avatar for previous tweets will NOT be 'repaired').

I think, this is clear enough