Believe me - this is a situation that is as frustrating for the TA as it is for the B&G.
Many people do not understand the difference booking through the established group can make either in benefit to the B&G or to themselves once they arrive for the function.
It depends on your TA whether or not they will book the flights as well - you should check to be sure. But in the US (and I think the airlines are handling their rates the same everywhere, it may not be possible to "lock in" a great package that includes air - fare pricing is dynamic (meaning constantly shifting with demand and availability). And a "deal" may not be a bargain at all.
That being said, the group rate is often an enticement to have guests book within the established block. The B&G get credits and extras based on the number of guest reservations - that's a big benefit to them.
Often, the guests will get better pricing and more amenities this way that would not be available to them when booked another way - even at the same property.
The wedding coordinator is working with the reservations staff to coordinate the numbers and it may confuse the issue to have guests booking outside the group. It is definitely harder to track the numbers that way.
The property is using those numbers to establish how many rooms can be held for that event and for how long. So when people book outside, it artificially inflates the demand and could serve to influence the numbers. In addition, rooms made through 3rd party on-line sources may or may not result in the reservation the person expects . If the hotel is oversold for that time period the guest could find themselves in a very different room category than expected (an Oceanview may become a really nice look at the parking lot) and paid for or, worse they could be "walked" to a different property nearby.
It is human nature to want to get the "best deal" but the best way to ensure your guests have a seamless experience without unexpected surprises when they are coming to attend an event, is to have them book within the established group block. But they need to understand "what's in it for them" so….
You may want to speak to your TA and ask about the group rate and amenities you have and what you could tell guests to help entice them to book in the block you have established.
Hopefully, it will be a win-win for everyone.