When does customer meet with the product?
When does the customer check the product if it meets with requirements? Is it after each iteration or after each release?
What would a customer "check" a product for, if his or her interests are represented by the Product Owner and each increment meets a Definition of Done of release quality?
What helpful inspection and adaptation opportunities are created by allowing the customer to "check" the product?
Does the Scrum Guide define any moments where such inspection and adaptation could be particularly effective?
Is there anything in the Scrum Guide that prevents this happening at other times?
As often as possible.
The Product Owner is responsible for managing the Product Backlog, which includes clearly expressing Product Backlog items and optimizing the value of the work performed by the Development Team. This requires some level of understanding of what the customer is paying for and what people who will be using the product want and need. The Product Owner works closely with the Development Team (or Teams) building the product, there can be a close-to-real-time level of feedback.
However, the Product Owner probably needs to communicate with various stakeholders, including the customer and users. This can happen as often as necessary. Sometimes it's very frequently, other times its less frequently. It depends on the relationship between the organization building the product and the various stakeholders. If you're building something for internal use, for example, and your customers and users sit down the hall, that is different than if your stakeholders are Fortune 500 enterprises or a global segment of the world's population. There are various techniques for sampling stakeholders if you need to.
The Sprint Review provides a common point to explicitly synchronize with key stakeholders. The Product Owner is responsible for inviting these key stakeholders to participate in the Sprint Review process. Again, depending on who your target audience for customers and users is and what is being reviewed, who is considered a key stakeholder may change.
I would suggest that if you aren't connecting the Scrum Team with stakeholder voices outside of the Scrum Team at least once per iteration, at the Sprint Review, you may want to rethink your Sprint Review process. However, your Product Owner, and perhaps even the Development Team, may benefit from more frequent interactions if it's feasible.
Early and often.