I assume you are talking about sending messages on italki (not sending messages on Skype).

If you are talking about italki messages, continue reading...

First... If you look at a member's profile, you will see "Send Message" in th upper right hand corner of the page. That will indicate that the member has chosen to receive messages from 'anyone' or only 'from friends'.

Second...Ask the person who you sent a message to to check their "Account Settings" (click on the profile photo or icon at the top of the page)

Then they can look at Privacy and Notification.

In the Privacy settings, people can select 'receive messages from (1) anyone or (2) friends only.

I have my Privacy setting set to allow anyone to send me a message.

So, if you send me a message, I should receive it and I will let you know that I have received it.