TL;dr - Speak to a local consumer rights organisation on this one before giving up hope or doing anything else.
Contrary to what the other answers have stated depending on a number of factors, particularly if you happen to live somewhere with stronger consumer rights or used a credit card under terms of such a jurisdiction, there may be some alternatives. Take all of this with a pinch of salt however as you're not going to have an easy time winning any arguments here - everyone involved has a vested interest not to give any ground.
Before going any further it's worth pointing out that the terms here do make references to a "Self-transfer Guarantee", so definitely double check the specifics of your booking because that would clear things up simply and conveniently for you straight off.
If our connection guarantee assistance services as outlined in this
section 8.2 (hereinafter referred to as the "Self-transfer
Guarantee"") is included in your booking this will be clearly stated
during the booking process and on your booking confirmation.
So there's a few scenarios where you may have some recourse still.
Firstly you may be able to argue that the terms of the contract are that others have quoted are simply enforceable, for example in the UK there's this in the Consumer Rights Act 2015:
"A notice is unfair if, contrary to the requirement of good faith, it causes a significant imbalance in the parties' rights and obligations to the detriment of the consumer."
Note that I'm not sure this section actually applies to airlines or services, so if you want to go down this route definitely seek proper advice, e.g. from a consumer rights organisation (often free) or other professionals. Fundamentally as it stands though there's a significant imbalance here in the terms others have quoted. They create perverse incentives for FlightNetworks because they stand to make additional revenue out of every schedule change and potentially can influence or understand the likelihood of that much better than you as an individual.
Secondly you may be able to argue that for instance FlightNetworks themselves cannot escape Regulation (EC) No 261/2004 - if airlines and their agents could escape that using small print you can bet they would've done so by now.
"(12) The trouble and inconvenience to passengers caused by cancellation of flights should also be reduced. This should be achieved by inducing carriers to inform passengers of cancellations before the scheduled time of departure and in addition to offer them reasonable re-routing, so that the passengers can make other arrangements. Air carriers should compensate passengers if they fail to do this, except when the cancellation occurs in extraordinary circumstances which could not have been avoided even if all reasonable measures had been taken."
(They might try to argue for example that they're not an "authorised agent" here and so it doesn't apply, but that's probably a double edged sword because they'd also potentially be arguing they couldn't actually sell you the tickets in the first place!)
These are just a few examples of why it's not a clear cut scenario. In terms of how to proceed with this sort of approach you ultimately need proper advice, not just random people typing nonsense on the Internet. I'd brace yourself for them recommending you pay the fee initially (probably with some carefully crafted words about doing so under protest). Then in slower time they may suggest following up with some kind of action, either small claims court, or if you have something similar to S75 of the consumer credit act with your card issuer. (There were some notably consumer friendly judgments there in the past, see for example Mr M on page 6)
So, if I were in your position I wouldn't do anything without at least giving a local consumer rights group in your jurisdiction a phone call and sound things out to see what they recommend. Maybe you are out of options, maybe you aren't, but don't let strangers on the Internet who don't even know where you reside tell you that either way.