I have noticed, while looking at my page source, the characters
showing just after a
You can safely get rid of the tag in the example you have posted.
is known as the soft hyphen and is used to break words up across multiple lines in web pages. You would normally expect to see it in the middle of really long words in a paragraph the same as you would hyphenate a long word in a written paragraph to space it over two lines in case you run out of page as you write it.
As for how to remove it, you can open the web page up using your website editor, locate the tag and simply delete it from the file as you would any other text on a web page when you edit the page normally.