They are really only concerned with felonies and crimes involving moral turpitude, so I doubt the check incident will be a problem. This link is for the Chinese Embassy right down the road from you so you can check with them to see what you actually need. http://houston.china-consulate.org/eng/ (http://houston.china-consulate.org/eng/)
Visarite is a pretty good outfit also, I have used them in the past for 2 visas and my Affidavit of Marriageability Certificate needed for marriage in China.
Here is the guidelines for a Tourist Visa ( L )
L Visa
Documents showing the itinerary including air ticket booking record (round trip) and proof of a hotel reservation, etc. or an invitation letter issued by a relevant entity or individual in China. The invitation letter should contain:
(1) Information on the applicant (full name, gender, date of birth, etc.)
(2) Information on the planned visit (arrival and departure dates, place(s) to be visited, etc.)
(3) Information on the inviting entity or individual (name, contact telephone number, address, official stamp, signature of the legal representative or the inviting individual)