Yes, those bridle straps would be a real pain to replace as originally
done, but fortunately we have replacements available that are much
easier.  From the piano supply houses you can get either cork-tipped or
spring clip bridle straps.  The cork fits into the round hole in the
catcher through which your original straps pass (almost all pianos have
these holes).  The spring clips fit onto the dowel.

Larry Lobel
Virtuoso Piano Service