Regardless of how busy you are at work, I still want you to contact me.
It doesn't matter how busy you get at work, I still want you to call me or send me a message..
ーRegardless of how busy you are at work, I still want you to contact me.
「仕事でどんなに忙しくても、連絡はしてほしい。」
regardless of で「〜にかかわらず」
contact で「連絡する」
ーIt doesn't matter how busy you get at work, I still want you to call me or send me a message.
「仕事でどんだけ忙しくなっても関係ないわ。電話かメッセージしてほしいの。」
It doesn't matter how busy you get で「どんなに忙しくても関係ない」
call「電話する」
send someone a message 「人にメッセージを送る」
ご参考まで！
カナダ 
