Can one bite into a fruit, such as a grapefruit peel, in order to start peeling it for immediate usage on Shabbat and/or Yom Tov?

ב"ה Shalom You may bite into the fruit if you want to, but there is no need to. An orange a grapefruit or a banana and their likes , are all foods which are inaccessible without removing the peel, and therefore the peel may be removed normally with a knife, (See Shemirat Shabbat kehilchata 3:35) and you may even make marks into the grapefruit into make it easier to peel. All the best