Well, if I can chime in from the ‘Old World’. It is highly appropriate to pay the priest for a mass intention–the amount is usually fixed by the diocese, 16 euros where I live, the amount is symbolically the amount a typical person in that area spends in a day. In many parts of the world this is the primary way priests support themselves.
So that’s one reason for the practice–it’s a way for the laity to materially support priests. But it also supports priests morally. It expresses in a concrete way that we need them and their priestly ministry, and I’m sure that priests feel enriched in their ministry by having people come to them and ask them to offer mass on behalf of their intention. Otherwise it’s far too easy for priests to feel isolated in this increasingly secularized world.
Another reason for making an offering for a mass intention is that it creates a moral obligation for the priest: since he has accepted money with the promise that he would offer a mass for your intention, he has to really do it (on pain of sin). This gives us something of a ‘guarantee’ that we wouldn’t have otherwise.
It hasn’t come up here, but another objection people sometimes have is why giving an offering for, say a novena of nine masses should be better than only offering one mass. It’s for these same two reasons: it’s that much more material and moral support for the priesthood, and because the priest is spending more time praying for your intention. Now of course there’s a lot more to prayer than the time we spend doing it, but all things being equal, we tend to do better, as mortal beings who exist in time, when we dedicate more time to prayer than when we only spend a little time. (God, on his end, is not limited by time, and can answer our prayers before we even have time to put them into words if he wants to, but on our end we are often helped by making use of the gift of time to united our wills more perfectly to his.)
All that said, of course, you cannot literally buy a mass (the mass being infinitely valuable, there isn’t enough money on earth!), nor can a priest say a mass for money without committing the sin of simony. The church’s practice is different, though: the priest is going to say mass anyway, whether anyone pays for him to do so with a specific intention or not. And the money, which is a largely symbolic gesture of support anyway, is no prerequisite–priests wouldn’t deny to offer a mass for someone’s intention if they couldn’t afford it, and I imagine most priests offer mass most often for intentions they choose on their own (and receive no offerings for).
So for the OP, if your grandmother wants a mass offered for the intention of your marriage, that’s highly appropriate (if it’s what she wants to do). Indeed, you might wish to do so yourself, on important anniversaries, or if ever you guys go through a rough spot and want to turn to the Lord for help. (Over here the more common popular misconception is that mass offerings are only for the deceased, whereas really any intention you might want to make a novena for could be a good candidate for a mass offering.) But it isn’t ‘fixing’ your marriage as if it were deficient in some way–and it’s a shame if she thinks it is–it’s merely arranging for the holy sacrifice of the mass to be offered to the Father, and for the benefits for doing so being applied to bless your marriage.
Mass offerings certainly aren’t required, nor are they the only tool we have as Catholics to bring our petitions to God. But they are one of the **best **ways, and I think it’s definitely a mistake to ignore them or think of them as an outdated practice.
