In looking at the context, I would have to say that by adding the words "and were filled" or "and were satisfied" would just add to the magnitude of the metaphor on display here through the parables and the feeding of the 4000. Matthew 15 is a contrast between the faith of a Gentile and the hardened hearts of the Jews.
Jesus was always teaching in parables to test the listeners to see if they could discern the spiritual meaning from the physical story. The common people understood but the spiritual leaders could not understand. The disciples also, on many occasions could not understand His parables requiring Jesus to explain the parables to the twelve. Here is Matthew 15 we have a prime example.
Look at the context starting in verse 1 (all verses KJV):
Then came to Jesus scribes and Pharisees, which were of Jerusalem,
saying, 2 Why do thy disciples transgress the tradition of the elders?
for they wash not their hands when they eat bread.
10 And he called the multitude, and said unto them, Hear, and
understand: 11 Not that which goeth into the mouth defileth a man; but
that which cometh out of the mouth, this defileth a man. 12 Then came
his disciples, and said unto him, Knowest thou that the Pharisees were
offended, after they heard this saying? 13 But he answered and said,
Every plant, which my heavenly Father hath not planted, shall be
rooted up. 14 Let them alone: they be blind leaders of the blind. And
if the blind lead the blind, both shall fall into the ditch. 15 Then
answered Peter and said unto him, Declare unto us this parable. 16 And
Jesus said, Are ye also yet without understanding? 17 Do not ye yet
understand, that whatsoever entereth in at the mouth goeth into the
belly, and is cast out into the draught? 18 But those things which
proceed out of the mouth come forth from the heart; and they defile
the man. 19 For out of the heart proceed evil thoughts, murders,
adulteries, fornications, thefts, false witness, blasphemies: 20 These
are the things which defile a man: but to eat with unwashen hands
defileth not a man.
Jesus responds to the query of the Pharisees about eating bread without washing their hands. Jesus explains that what goes into a man does not defile the man but what comes out of the man defiles him. The disciples, who are “dull of hearing” just like the Pharisees, do not understand the parable and ask the meaning in verse 15.
So we see that the disciples are still having trouble gaining the spiritual meaning from the teachings of Christ.
Let’s move to the next set of verses.
22 And, behold, a woman of Canaan came out of the same coasts, and
cried unto him, saying, Have mercy on me, O Lord, thou son of David;
my daughter is grievously vexed with a devil. 23 But he answered her
not a word. And his disciples came and besought him, saying, Send her
away; for she crieth after us. 24 But he answered and said, I am not
sent but unto the lost sheep of the house of Israel. 25 Then came she
and worshipped him, saying, Lord, help me. 26 But he answered and
said, It is not meet to take the children's bread, and to cast it to
dogs. 27 And she said, Truth, Lord: yet the dogs eat of the crumbs
which fall from their masters' table. 28 Then Jesus answered and said
unto her, O woman, great is thy faith: be it unto thee even as thou
wilt. And her daughter was made whole from that very hour.
Here we see a perfect example of a Gentile follower of Christ who can very easily discern the spiritual principals of Christ’s parables. When Christ tells her that it is not proper to take the “children’s bread and cast it to the dogs”, she immediately responds properly discerning the spiritual application. Christ’s reference to bread is not physical food but spiritual food. The woman understands this and responds that even the family dog (Gentiles) desire to feed on the “crumbs” of spiritual food (His teaching) that fall from the table of the Jews.
Jesus immediately is impressed for this Gentile woman has demonstrated that she is led by the Holy Spirit and demonstrates great faith in Christ and His teaching.
Now contrast the “crumbs” of the Gentile to the “and were filled” passages of the feeding of the 4000.
32 Then Jesus called his disciples unto him, and said, I have
compassion on the multitude, because they continue with me now three
days, and have nothing to eat: and I will not send them away fasting,
lest they faint in the way. 33 And his disciples say unto him, Whence
should we have so much bread in the wilderness, as to fill so great a
multitude? 34 And Jesus saith unto them, How many loaves have ye? And
they said, Seven, and a few little fishes. 35 And he commanded the
multitude to sit down on the ground. 36 And he took the seven loaves
and the fishes, and gave thanks, and brake them, and gave to his
disciples, and the disciples to the multitude. 37 And they did all
eat, and were filled: and they took up of the broken meat that was
left seven baskets full. 38 And they that did eat were four thousand
men, beside women and children.
The disciples had just experienced (recorded the chapter prior) Christ feeding the 5000. They had just seen Christ feed that multitude and still the disciples ask Christ “where are we going to get the bread to fill these folks out here in the wilderness”. Clearly the disciples are exhibiting an incredible lack of faith.
These accounts demonstrate the stark contrast of living under the law by the Jews verses living without the law by the Gentiles. This is a great metaphor showing the hunger for Christ by faith as demonstrated by the Gentile woman looking of any “crumb” of Christ that she could get verses the Jews who “were filled and they took up of the broken meat that was left seven baskets”. The gentile woman was physically needy but she is spiritually rich. The Jews/disciples are physically gorging themselves but are still spiritually starving.