Unless you have a combined foul/rainwater sewer, rainwater would usually be dealt with separately. It should go to a soakaway. This does sound like a bodge, especially with the irregular hole.
I guess this "connection" is right underneath the extension?
Even if it's a combined sewer, the connection should be accessible via an inspection point in the extension floor. If not, then it is a bodge.
If I've got this right, there are really only two things you can do.
Cut through the extension floor to get at the connection, or have a specialist company re-line the inside of the foul drain, thus sealing off the rainwater entry.