Sh'mot 8:7:
וְסָרוּ הַצְפַרְדְּעִים, מִמְּךָ וּמִבָּתֶּיךָ, וּמֵעֲבָדֶיךָ, וּמֵעַמֶּךָ: רַק בַּיְאֹר, תִּשָּׁאַרְנָה.
Artscroll says it means "depart", implying the frogs will hop away. A few p'sukim later the frogs just drop dead. Although they do physically leave the houses, it is because they are being cleared away by humans.
What did G actually say concerning frog removal? Was he intending on being technically within the letter of his promise (in the manner of Lavan cheating someone)?
According to the Sforno on 8:7, the pasuk says that they will be removed from the houses
but not from the whole country; on the contrary, they will die in the land and cause a stench, but in the future they will not leave their habitat in or near the river.
The Malbim indicates that the pasuk indicates the order of the removal (which, I guess, means that after they stank, then they were removed, since m'amecha is 4th).
The Shadal draws a different distinction
כמו וסר מהם הנגע, ואין הכוונה שילכו להם חיים, ולפיכך לא אמר רק אל היאור ישובו, אלא ימותו במקום שהם; והכורם טעה בהבנת מלת וסרו, וחשב כי משה הבטיח שישובו אל היאור חיים, וה' לא רצה.
That the "remove" wasn't a physical removal, but a "remove the plague" which just means the frogs would die and stop being a plague.
This is echoed by the Tur Ha'aroch on 8:9 regarding the death of frogs
How do we square this with verse 7 in which Moses predicted the frogs as “departing?” Moses had referred to the frogs as a plague departing, he did not predict that they would depart under their own power, as did the locusts in the eighth plague. On this occasion the dead frogs remained wherever they had died.
A bunch of the commentators point out that the ones in the ovens did not die.
All citations from Sefaria.
According to the Targum Onkeles, סרו is an expression of restriction, like יסר or אסר. The actual targum is ויעדון from the root יעד which means the frogs were given a designation, like when a women is betrothed to her future husband, she is designated to him and not others. That originally she is available to all men, but then restricted to her betrothed.
The frogs were implanted with a particular purpose that did not involve Pharaoh, nor his home and property or his people.
This means that what Moshe was demonstrating was that G-d can change the instinctive nature of all things. That is why the two names of G-d, that pertaining to what transcends nature and that which pertains to nature were referenced by Moshe when addressing Pharaoh.
The frogs operate only according to their natural instinct, their innate behavior. Their normal instinct is to behave as an amphibian and live in and near the water. That innate behavior was changed and is what brought them to Pharaoh at the time of the plague. G-d again changed the innate behavior of those frogs as a consequence of Moshe's prayer and they had no further interest in Pharaoh. They returned to their original instinctive behavior as amphibians.
