I was recently offered a verbal offer to join a PhD lab group with a professor that I had taken classes with during my Master of Science program. I did well in the said professor's classes, and I was asked if I would be willing to do a PhD. I was also verbally offered that the professor would be willing to admit me to the lab group.
I sent my transcripts and other information as requested, and explained my grades which are not good during undergrad. However, the professor has also taught my classes during the Master's and I did fairly well in those classes, and demonstrated my research experience during those classes as well.
However, since the professor wants people with exceptional GPAs, I am not sure if my verbal offer (via email) would be rescinded. I have not heard back anything since my email explaining that I did mess up in undergrad, but I have improved and I am committed to tackling the PhD in the lab group.
I am very interested in joining the PhD, but I also don't want to get my hopes up (since a willingness to admit me which the professor mentioned via email is not a written, official offer for admission to the PhD lab group). However, I am not sure what to do, as I don't want to keep prodding on the subject matter and forcing the professor to give me a response when the professor may be busy/thinking about about me to the lab group.
What is a way I can approach this, in order to demonstrate a) I am very interested in joining the group to pursue my PhD and b) I am confident that I will have the capability and willingness to learn and improve?