I have never heard this phrase. I think it typed incorrectly. Possibly should be "suit my image". In that phrase, suit means "fit" or "go with" .
For example, when 2 people get married, one may say they are "well suited" or "they fit together well".
Another example is "That color does not suit her", meaning it is not a good color on the woman (could be clothing or lipstick or even hair color)
So, a respected lawyer would think that a t-shirt and jeans does not "suit her image". It does not fit with the appearance she wants others to see. She wants to be seen as intelligent and powerful.
Or an young person would not think that a more conservative style "suits their image".
Your image is what you want other to see when they look at you.