inferior strop

a cheap strop should not hurt my razor correct? I have one made by Hashir. Attachment 345242

As long as it's smooth it won't hurt the blade.

Can't be worse than a leather belt.!

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If you have the opportunity to compare it to a quality strop that would answer the question much better.
Personally, all of the low priced strop's that I have seen are not good for razors. The surface texture feels "coarse/pebbly".
It is dismaying to spend all that time honing a straight razor only to find out that the strop is reducing the sharpness of the edge.
May I suggest that you first hone the razor and then test shave with that edge. After that use the razor on the strop and test shave again.

I have costly strops from a prized Kanayama on down

My work strops are almost all Illinois 827's (Med Heavy Draw) I have bought probably 15 over the years never more than $40 shipped to the house, that and its Cousin the #127 (Light Draw) are what I always recommend when asked

For that price they can't be beat, the Linen is VERY effective also

ps: You sometimes find them listed under the name Fromm, same strop Fromm is the parent company, it will be an Illinois brand

I would trust a cheap strop from a company that has a 100 year old reputation to lose, like Illinois.

I have another strop from a seller (who also happens to be a strop maker) on eBay that I bought a razor from, and he tossed the strop in for free. I use it on kitchen knives. It's not smooth at all, and has a wrinkled finish from where the hide was folded at some time before becoming a strop. I wouldn't dream of using the leather side for razors.