How Bil'am tried to foment a war by adding one letter

Balak told Bi'am that  הִנֵּה עַם יָצָא מִמִּצְרַיִם, while Bil'am reported the conversation to Hashem as
הִנֵּה הָעָם הַיֹּצֵא מִמִּצְרַיִם

Rashi, reports on the other obvious strengthening of the words of the report in order to inflame matters, but we see that just changing one letter can cause the impact of the report to be completely different.

According to Rav Hirsch, Balak said the main situation was not that this was a particular people, but that a people who had been completely submerged in the power of the Egyptian Empire had wrested themselves free and were now going to completely destroy the surrounding nations (even if they are not going to attack Moav directly).
Balak 22:5

הִנֵּה עַם יָצָא מִמִּצְרַיִם The repetition of הִנֵּה shows that with עַם יָצָא מִמִּצְרַיִם a separate thought is given for his consideration. The fact that עַם יָצָא מִמִּצְרַיִם, that a mass of people politically and socially submerged in the power and nationality of Egypt could go out of Egypt as a socially united people to freedom and independence, marks this people as something unique. And it is to the cause which could have effected this remarkable unheard-of event which your mind must concentrate on, if you are willing to help my purpose to be achieved.

On the other hand, Bil'am knew who they were and what was occurring as a result of Hashem's specific will. He knew that it was not some random people showing the breakout from Egypt, but was the people, the specific people that Hashem had taken out גוי מקרב גוי and the answer to Balak's request as asked would be Tell Balak not to worry, they are moving at my explicit command and will not invade you. Bil'am, on the other hand wanted to see them destroyed and actually tried to get Balak to fight them. As Rashi says on Balak 22:11

curse it: Heb. קָבָה לּי. [This expression used by Balaam] is stronger than אָרָה לּי [used by Balak in verse 6], for it specifies and details [the curse]- [Mid. Tanchuma Balak 5, Num. Rabbah 20:9]
and drive it out: of the world. Balak said only, “and I will drive him out of the land” (verse 6). [His intention was:] I want only to get them away from me, but Balaam hated them more than did Balak. — [Mid. Tanchuma Balak 5, Num. Rabbah 20:9]

Thus, Bil'am referred to this people in order to avoid any possibility of it being someone or something other than Bnai Yisrael as well as to avoid the possibility of being told to reassure Balak that they would not invade Moav and would not need to be fought off.