Modifying response body is not natively supported by Varnish. You need a Varnish module (vmod) for this.
Aivars Kalvans has libvmod-rewrite, which does exactly what you are looking for. However the vmod is a proof of concept and according to Aivars it is not ready for production use. You can use it as a starting point in any case.
If you are using Apache, you can use mod_ext_filter to modify response body. Here's an example from mod_ext_filters documentation. Since you can pass the response body to any external command, it is very easy to do the necessary modifications to the content.
# mod_ext_filter directive to define a filter which
# replaces text in the response
#
ExtFilterDefine fixtext mode=output intype=text/html cmd="/bin/sed s/verdana/arial/g"
<Location />
# core directive to cause the fixtext filter to
# be run on output
SetOutputFilter fixtext
</Location>