It could a slip of the tongue. Or the speaker finds she has fully expressed her meaning after the utterance of shite.
It is not rare in daily conversation and, not a surprise, used in a light-novel dialog.
十香 draw 士道's attention (maybe looked around or changed his facial expression) and 十香 is explaining why he took such behavior.
If you use 気がしてな, it sounds like "(I'm doing this) because I feel like someone is watching us."
If you use 気がする, it is more simple, "I feel like someone is watching us."