There is not anyway to pull it up and look at it without going there. However when you end a crucible match/turn in a bounty/finish a patrol mission when you see the +x points for the reputation there is a circular progress wheel that shows how close you are to the next level. You can see if you are high enough level to buy gear from the vendors through the companion app/website. Just go to the tower section and click on the vendor. Look at the item. If it has a checkbox next to rank lvl 2 than you at least know your level is that high. It's not perfect but it's something. I would like them to add this to the legend section of the companion app/website.