Awe and love leave an imprint that awakens teshuvah

בשם אא"ז מו"ר ז"ל שהגיד עמ"ש פותח שער לדופקי בתשובה כי הם האבות אברהם יצחק ויעקב נקראו דופקי בתשובה.

In the name of my grandfather, my master and teacher, of blessed memory, who said regarding the words "He opens a gate for those who knock in teshuvah" — that they are the Avos, Avraham, Yitzchak, and Yaakov, who are called "those who knock in teshuvah."

The Sefas Emes cites his grandfather's teaching: the liturgical phrase about Hashem opening a gate for 'those who knock in teshuvah' refers to the three Avos.

והדברים עתיקים דפח"ח.

And these are deep, ancient matters — words from the mouth of the living [are beautiful].

He marks the teaching as profound and beautiful (the abbreviation expressing praise for fine words of Torah).

ומסתמא ע"י מידותיהם יכולין גם אנחנו להיות בכלל דופקי בתשובה.

And presumably, through their middos (character traits), we too can be included among "those who knock in teshuvah."

Since the Avos bequeathed their spiritual middos to their descendants, by drawing on those inherited traits we can also become 'knockers in teshuvah' and have the gate opened for us.

והוא מ"ש קחו עמכם דברים שע"י התורה בדחילו ורחימו וז"ש עמכם כי כל מצוה ותורה שהוא בדחילו ורחימו נשאר ממנו רשימה בלב האדם ועי"ז זוכין לתשובה כנ"ל:

And this is the meaning of "Take words with you [and return to Hashem]" (Hoshea 14:3) — that through Torah performed with dechilu u'rechimu (awe and love), and this is [the meaning of] "with you," for every mitzvah and Torah done with awe and love leaves an impression (reshimu) in a person's heart, and through this one merits teshuvah, as above.

The verse's word 'with you' is the key: any mitzvah or Torah done with yiras Shomayim and ahavah leaves a lasting imprint on the heart. That inner residue is what a person 'takes with him,' and it is what later awakens him to teshuvah.

Summary: The Avos are 'those who knock in teshuvah' for whom Hashem opens the gate, and through their inherited middos we too can join them. The verse 'take words with you and return to Hashem' teaches that Torah and mitzvos performed with awe and love leave a permanent imprint on the heart — and it is this inner residue that we carry with us and that ultimately awakens us to teshuvah.