I know a bit about HPV because it is a very widely studied virus across many social and physical science fields, easily transmitted, and I worked for about a year in the study of STD transmission.
First, condoms do not (repeat DO NOT) eliminate the risk of transmission. However, men are at much lower risk for infection than women. It is estimated that somewhere around 75% of women will contract HPV in their lives (in America) and most of them will have it cleared by their system without ever knowing that they had it. That sounds like what happened with your girlfriend, except she knew about it for some reason. Have you asked her how she discovered she had HPV? That is unusual. So, I guess it is similar to saying "My girlfriend contracted flu 7 years ago, do I need to worry about this?" (Answer: No.)
There are many, many strains of HPV, and some are no big deal and some need to be taken more seriously. At least 4 strains are known to cause cervical cancer in women, which is why young girls get the vaccine here, but bizarrely it is not offered to young boys. (Where do most of these girls get HPV?? Most public health workers disagree with this policy but are powerless to change it.) Public health workers have long argued for cervical cancer to be classified as an STD because over 95% of cases can be traced to this virus. It almost never causes cancer in men, but I guess there are a few rare instances. If it is totally gone from her system, I think you're fine. Could you ask your nephrologist just to be safe?
Oh, and just because condoms do not stop the transmission, they do reduce the risk somewhat, and as a mom of two boys I feel I would be remiss if I did not mention that I think these should always be used at this stage of a relationship, both for safety and to avoid extreme complication in your life, if you get my meaning!