The phrase "I know you're busy" shows understanding and consideration for the other person's time and commitments. It acknowledges that they have a lot going on in their life, but despite that, the speaker wanted to reach out.
The statement "just wanted to let you know I am thinking of you" expresses a genuine connection and a desire to maintain it. It's a sweet and affectionate way of saying that even in their busy lives, the person is always on the speaker's mind, and they wanted to remind them of their presence and importance.
In summary, this message is a warm and considerate gesture that reaffirms the value of the relationship and the speaker's genuine care and affection for the other person, even when they have busy schedules. It's a reminder that thinking of someone and reaching out can strengthen and nourish a connection, no matter how hectic life may be.