I know of plenty of business who print their own checks, but they order their own unique paper... Imagine if large franchises or large corporations had to buy checks from the bank just to pay their employees... It'd be really expensive. You can pay with a check without even providing a check too - give routing number, account number, amount, name, and sometimes a signature to an online company and they'll use that information to initiate a transfer of funds... The check number just becomes a reference number.
Now, if the bank account number and routing, swift or ABA or whatever is correct then it could be the user got the companies information out of the trash or some other means and is using it to write bogus checks which the company will eventually discover and either return, or if it is too late to return they will come after you...
The large amount of money over what you would normally charge may support the idea that it is going to a country with sanctions and it makes YOU look complicit as though you're taking a bribe or payment to allow it, or to look the other way to let it happen....
NEVER take an order from a business without an official order form request from them signed by someone in charge of orders with a phone number you can call which is registered to them that you can call to confirm the order. If it is a company out of the country then they need to state what the product will be used for - at the very least they will need to sign a document claiming they will not send it out of the country ( I know Harbor freight and other companies in the USA does this - a family member of mine from Germany came and was denied being allowed to buy a ball peen hammer because he wanted to take it with him to Germany and that particular hammer wasn't allowed to be exported to Germany for some reason - turned out it was a mistake and he got the hammer, but a few other items he wasn't allowed to buy )....
I'm pretty sure, by law in the United States, if you take an order knowing it is being exported out of the country you need to do all of this extra paperwork... It happened at like 3 stores we went to...