Which is correct grammar the couple know or know?

The correct grammar depends on whether the couple is considered a single unit or individuals.

If the couple is considered a single unit:

* The couple knows... This is correct because "couple" is singular and takes a singular verb.

If the couple is considered individuals:

* The couple know... This is correct because "couple" is plural and takes a plural verb.

Example:

* The couple knows how to dance the tango. (The couple is acting as one unit)

* The couple know each other very well. (The couple are two individuals)