No solution will be provided since there is no mechanism that removes staff specialties. It was never there. Maybe you have had the trainer for so long (you did buy him last year) that you forgot you bought him without a specialty.
I guess i was not clear enough when a said:
"
Nope, Always use the filters when looking for new staff members. And double check during bid wars. Told you since Season 19 i only had trainers with career extension because my team had a lot of Vets.
Last seasson, in mid seasson the traineer had a speciality.I don't know how it happened. Seriously. But I need a solution."
If you look at my roster you can see why i have several seassons buying traineer with career extension. Again, I always use the
filters when searching for new staff members and
double check during bid wars. I Not buy him with no speciality, he has career extension during the seasson

.