Two considerations embedded in the initial question are the role of test scores and the role of extra credit.
A basic general goal in math teaching is that we want students to learn to “do math” accurately, understand the concepts, and (perhaps most importantly), to routinely practice what they learn. Tests often do well in evaluating the first two goals, but tell us little about the third. Some students who can do well actually do so on tests, but don’t want to trouble themselves to work neatly and accurately in daily lessons. Some measure of including daily work as part of the score can help to build the life skill of diligently and routinely working carefully.
The primary goal of extra credit work (even as it boosts the student’s overall score) should be to encourage even more learning. One form is additional worthwhile practice, which can serve to strengthen skills. Another is work that “goes beyond” which in math might mean pursuing application problems that extend the subject into practical applications that the routine course might not supply.
If the primary problem prompting the teacher to look for extra credit opportunities for the student is an occasional “blown” test score, you might want to try offering a retest with another form of the test (the same type of questions, but different questions).