Unfortunately you can't push the pegs through because the other ends are completely enclosed by the seat and lid.  Each peg has a very small lip at the exposed end that provides some purchase and can help to get them moving.

I found this thread useful when trying to fix a GSI Panorama seat. It is a case of pulling out the horizontal metal pegs, which have no cap at the end or screw thread inside. I was able to extract one trying a series of tools:pliers, screwdriver, hammer. The other refused to budge, even using a mallet and screwdriver to try and chisel it out with some force. I ended up pulling out the whole fixing from the hole in the ceramic part of the loo. It was very corroded and I think this type of fixing is unsuitable for a hard water area.Even with the seat off I couldn't get the peg out.I ordered a new seat with soft close hinges and this while also having the awful butterfly clips, which I dreaded losing down the hole forever, at least does not have the same problem with the hinges