Deference is more precise then tact for blank 1.

The should be (C)deference & (F)denigrating
If not, Please explain.

Her performance review noted that Jill suffers from a lack of ____(i)____, and often makes insulting remarks despite her best efforts to be polite;

she was uneducated so she did not have tact or i.e she was not polite

worse, the review went on to point out that it happens regularly, even though she has no intention of ____(ii)____ anyone.

denigrated is the only other word that fits the bill

Hope now is more clear than before

Regards

I still can't understand why tact is right

My thought process was that tact means skill in dealing with difficult situations and deference means respect

It's mentioned that she was impolite. Out of the two, lack of deference (respect) seems closer to lack of tact

Tact is more specific than deference, meaning delicacy, fit and acting well according to the environment.

Jill tries but is unable to be polite. In this case, she is not sensible. Therefore, tact fits the blank here.

IMHO, if this line were not to be there, despite her best efforts to be polite , then deference should fit the blank.