Hi! In my opinion, deleting or not texting back is the same type of response. I would recommend you out yourself in the other person' shoes. I would prefer someone telling me that they have too much going on to start a new friendship, instead of ignoring me. Hope it helps! 

Telling them straight, if it doesn't work, you just don't give them no more chances to be friends with you.

If you have just received a request either ignore it or politely reply that you already have enough partners.

If you have already accepted a request from someone, and then change your mind, I suggest that you tell them that it will be difficult to continue exchanging with them because of changes to your work schedule.  This can be done whatever the reason for not wanting to continue.

I feel that simply not replying is a bit rude, although it does sometimes happen accidentally if you have a busy schedule.

It doesn't matter what kind of relationship it is between you two. 

@Yannick

It sounds like dealing with a relationship...

Just friends.