expression, ichidan verb
have a secret sexual relationship; have an illicit love affair
A euphemistic set phrase for a clandestine sexual relationship, often implying adultery or a socially disapproved affair. The expression uses 慇懃 (courtesy, politeness) ironically to suggest outward propriety masking an intimate liaison.
二人は長年慇懃を通じていたが、ついに周囲に知られてしまった。
The two had been carrying on a secret affair for years, but finally people around them found out.
The phrase combines 慇懃 (courtesy, politeness) with を通じる (to communicate, to have relations with). The ironic use of 慇懃 suggests that outward politeness or formality hides a secret intimate relationship. The exact origin is uncertain, but it is a well-established literary euphemism.