Hi Sprockets,
To start, a 670/Q44 is a solid Score, so it could be enough to get you into your first-choice School. As such, another retest might not be necessary. Depending on the Schools that you plan to apply to, you would likely find it beneficial to speak with an Admissions Expert about your overall profile and plans. There's a Forum full of those Experts here:
https://gmatclub.com/forum/ask-admissio ... tants-124/Both a Q44 and a Q42 mean that your general math knowledge is good - and you properly dealt with most of the 'math' questions that you saw on the GMAT each time you took it (and I wouldn't be surprised if you scored in the low-Q40s on your At-home GMAT). However, the Quant section of the GMAT is NOT a 'math test' - it's a 'critical thinking test' that requires lots of little calculations as you work through it. To score at a much higher level in this section, you need to become more of a 'strategist' and less of a 'mathematician' - otherwise you will likely continue to score in the low-Q40s.
As an aside, there are other ways to 'offset' a lower GPA besides a higher GMAT Score, but before we discuss any of those alternatives, it would help if you could provide a bit more information on how you've been studying and your goals:
1) What study materials have you used over the course of ALL of your studies?
2) On what dates did you take EACH of your CATs/mocks and how did you score on EACH (including the Quant and Verbal Scaled Scores for EACH)?
3) When are you planning to apply to Business School and what Schools are you planning to apply to?
GMAT assassins aren't born, they're made,
Rich