Is it me? I see the pic as being terribly underexposed.
But to solve that trick, you need to light on 2 different planes. Three tier is nicer but for this issue that you bring up, just shoot A-your subject and B-your background with separate lighting.
One plane:
Two plane:
Once you learn to control each aspect correctly, you move on to the next. Example, you don't move on to the back lighting until your subject is properly exposed. I like to under expose the background by 3 stops (makes it pretty much BLACK), then toss in a little backlight that
*matches* the keylight exposure strength (NO shadows!

). I overexpose the hairlight in a 3-tier setup by around a half stop over the keylight (subject). In the 2nd pic, you can tell I was about a 1/4 stop off or aimed the back light about 6-10" too low (you can tell there is a slight shadow of the bear's head/ears on the backdrop).
To reduce the need for a strong backlight:
1 - move subject a little further away from the backdrop (5-7 feet)
2 - Bring the umbrella closer to your subject (within 3-4 feet
or less for a 40-45" umbrella). The increased apparent light size will soften the shadows in the rear tremendously.
3 - It should not be needed, but if it is, a reflector can be used to remove the last tinges of a shadow if needed.
If you did the Lighting 101 exercises, it would be a little clearer, as they touch on this indirectly. Look for "apparent light size" for a clear explanation... or if you don't find it, PM me and I will explain.
Oh... and get those wrinkles out of your backdrop! (lol)