There is no such thing as a generally accepted level.
There are various national standards from around the world.
Some only address total radiation, some only specific types.

If your customer cannot tell you what to measure then it isn't a specification, only a wish.

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Plymouth Tube

It sounds to me like you might be supplying a German customer. We have the same issue. We bought a small digital geiger counter from these people: http://www.anythingradioactive.com/geiger.htm

We measured background radiation in a number of locations around the shop. Anything that is shipped to Germany is checked before it leaves our site to see if it is contaminated. We also check all incoming raw material with the same machine.

The plan is that if any item shows higher than background levels it is quarantined and advice is sought from a qualified professional. So far, we have had no reason to contact him.

Remember, a Roentgen is a measure of ionizing radiation only.

Go back and ask them for a specific number that you must meet.
None is not a value.

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Plymouth Tube