Just in case you were wondering.
I use here the move notation from http://www.ibiblio.org/twixtpuzzles/
Link removal notation is by the coordinates of the link's center, with the apostrophe standing in for "half". For example, -E8' would refer to removing the link between F8 and D9, or F9 and D8, and -E'8 would refer to removing the link between E7 and F9, or E9 and F7. This is unambiguous for link removal, since links cannot cross, but for link addition, the distinction is made by preceding the letter with \ or /. For example, /E8' would refer to adding a link between D9 and F8.
When placing a peg, all legal links to that peg are automatically added. Such links are not explicitly mentioned in the notation.
Here is a variation from a game I recently played.
Purple to move could play -i5'i5
but then yellow wins with J4.
Under standard rules, the only winning move is i5 with no link removal.
Yellow is unable to prevent purple from adding the /H'6 link later. Play might continue with yellow playing at K4 to prevent purple from double linking from i5 to J6,
and then purple wins with -i5'/H'6K6
So, if you are writing Twixt software and you want to implement standard rules, don't forget to include this nuance.