"If it's too good to be true, it probably is" is not true when it comes to the Gospel. The Gospel is absolutely free. There are no strings attached. There are no ifs, ands, or buts with the grace of God. The Gospel is good news to the hearer. It is a declaration that all has been taken care of. Your sin has been atoned for. There is nothing left to be done.
An old hymn
An old hymn we sometimes sing at church goes like this: Jesus paid it all, all to Him I owe. Jesus did pay it all. He took the wrath of God for every sin I have ever or will ever commit. When He was on the cross God treated His Son as if He committed all of my sins. Christ absorbed "in His body on the tree" all of the wrath of God that I will ever deserve.
When Christ cried out on the cross "it is finished" OUR DEBT WAS PAID IN FULL! If all is paid what then is left for us to pay? Nothing! But what about the second part, "all to Him I owe?" The song is speaking about our service to God after He has so gloriously saved us. For sure it is not speaking about a sort of works righteousness. However, because Christ accomplished the work that I do owe God, I owe nothing. To even try to pay God back for His indescribable gift is an offense to his grace. He will receive all of the glory for our salvation. Even our works predestined for us to do are done by His grace. I owe God nothing. The debt has been paid in full.
Payment vs. gift
Paul makes this clear when he contrasts receiving payment for work we do and receiving a gift.
Romans 4:4-5 Now to the one who works, his wages are not counted as a gift but as his due. And to the one who does not work but believes in him who justifies the ungodly, his faith is counted as righteousness,
When I receive my paycheck at the end of the week I don't thank and praise my boss for his generosity. I take what I've earned. I worked for it. It's mine. However, if someone pays off a major debt that I owe I am filled with gratitude because of their generosity towards me. We have had our sin debt, a debt that is infinite, paid off in full by the death of an infinitely valuable Person, the second Person of the Trinity. So to try and pay God back, even in the smallest way is a great offense! Jesus paid it all so I owe nothing.