Overset and mathbb collision

While the accepted answer provides the solution, I wish to address the "Why?" issue in the question.

The \mathbb alphabet is defined by amsfonts.sty as

\DeclareSymbolFontAlphabet{\mathbb}{AMSb}

which basically means "use the glyphs from the font AMSb" (which is also declared by amsfonts). The font AMSb contains the blackboard-bold capital letters and a whole bunch of other symbols. So when you type \mathbb{T} you obtain what you expect; but \mathbb{m} looks for the glyph in the slot "6D, which is not a small blackboard-bold m (it doesn't even exist in AMSb) but rather the symbol \gtrdot, thus explaining the weird result.

You need to put the T inside the overset:

\overset{m}{\mathbb{T}}_{ij}