First, do not offer food that has already been on your plate or has been touched with your eating utensils (fork, etc) after you've taken a bite. For this to work it needs to be clear that the food you're offering hasn't been touched or eaten from directly - you served from a storage container onto another dish, ate from that dish, and your eating utensils haven't gone back into the food in the storage container.
Second, in sharing a meal you are sharing your company, not just food. Make it clear before you start eating that you have more food than what you'll eat, and others are welcome to it so that the offer is made before you start eating and 1) they can clearly see the food you're offering is untouched and 2) they will be eating with you, these aren't leftovers after you're done, these are elements of a shared meal. This should allay any fears about hygiene, as well as prevent them from feeling like you're doing charity or just getting rid of food you don't want.
Third, you need to judge how much you're going to eat prior to serving yourself, and only take what you plan to eat. You can always move food from the storage container onto your dish later, but you can't take food from someone else, so take what you need, offer the rest, and only take more if they've declined your offer or if they didn't take the remainder.
If those conditions are met, then a simple invitation should be enough, offered any time before you take your first bite:
I packed too much food, this (gesture to the container where the remainder is, perhaps describe what it is if it's not obvious) is available if you are interested.
When finished, pack up everything and thank them for spending time with you.