To understand why some translations omit Mark 7:16, first we need to understand a little bit about a process known as “textual criticism”.

In brief, the original versions of the NT books (known as the “autographs”) are no longer available (they no doubt disintegrated many centuries ago). The Greek text we have today is based upon copies, about 5000 different manuscripts. In general, these manuscripts all say the same thing and when there are differences they are mostly simple copying mistakes, like spelling mistakes. Occasionally there will be a more significant difference, and that’s what we find in Mark 7:16. Some manuscripts include it, some don’t.

The way scholars (or “textual critics”) try and decide which was original is using a number of different criteria, such as which are the oldest manuscripts, where did these manuscripts come from, is there an obvious reason for the mistake (like a copying error). In this case, the earliest manuscripts do not include Mark 7:16. Also the phrase “If anyone has ears to hear, let him hear!” is very common so it is conceivable that a copyist may have mistakenly added it in.