expression
A formal letter-closing phrase used to apologize for not mentioning something earlier in the letter. It conveys humility and is typical in Japanese written correspondence.
末筆ながら、皆様のご健康をお祈り申し上げます。
Finally, I wish you all good health.
末筆ながら、ご多忙の折、お返事いただければ幸いです。
Last but not least, I would appreciate your reply despite your busy schedule.
Compound of 末筆 (まっぴつ, 'end of a brush/writing') + ながら ('while, though'). The phrase literally means 'while it is the end of my writing', used to humbly introduce a final remark.