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Recommend you contact the seller and request your money back/ exchange... use that money to get a better strop, pitch in a few $. Get a smooth strop..
I understand the quality control is...

It's not a smooth strop. That said, my concern is that the edges look damaged, so I would not use it till figured out. As 10 Pups states, someone who knows this strop better will be along.....

Stropping:
http://www.youtube.com/watch?v=

As stated, I wouldn't do anything till you figure this out.. (ie what's going wrong and how to fix it)

I wouldn't use it. May well be fixable. Read this info from the library, read the links also:
http://straightrazorpalace.com/srpwiki/index.php/Razor_Strops


Likely can be repaired but read all...

I think you are stropping with blade at an angle- cutting the leather and hurting razor (or are you leading the edge?). Go see video on stropping, razor blade just follows so gently the spine... ...

I have that strop, not normal. NO more Fromm conditioner, use very sparingly... please post pics if you can!