The concept "pure oil" with regards to lighting the Menora in the Mikdash is explicitly defined in Menachot Chapter 8 Mishnayot 4 & 5.
Basically, the olives are squeezed but not crushed, producing oil that doesn't need to be filtered.
This fulfills the Biblical command of שמן זית זָך - pure olive oil - in that it was always pure and didn't need filtering to become so.
Here's the original, with Sefaria's unedited translation. ("candlestick" meaning the menora in the Mikdash)
ה זֵיתִים, וּבָהֶן שְׁלשָׁה שְׁלשָׁה שְׁמָנִים. הַזַּיִת הָרִאשׁוֹן, מְגַרְגְּרוֹ בְרֹאשׁ הַזַּיִת וְכוֹתֵשׁ וְנוֹתֵן לְתוֹךְ הַסַּל. רַבִּי יְהוּדָה אוֹמֵר, סְבִיבוֹת הַסַּל. זֶה רִאשׁוֹן. טָעַן בְּקוֹרָה, רַבִּי יְהוּדָה אוֹמֵר, בַּאֲבָנִים. זֶה שֵׁנִי. חָזַר וְטָחַן וְטָעַן, זֶה שְׁלִישִׁי. הָרִאשׁוֹן לַמְּנוֹרָה, וְהַשְּׁאָר לַמְּנָחוֹת. הַזַּיִת הַשֵּׁנִי מְגַרְגְּרוֹ בְרֹאשׁ הַגַּג, וְכוֹתֵשׁ וְנוֹתֵן לְתוֹךְ הַסַּל. רַבִּי יְהוּדָה אוֹמֵר, סְבִיבוֹת הַסַּל, זֶה רִאשׁוֹן. טָעַן בְּקוֹרָה, רַבִּי יְהוּדָה אוֹמֵר, בַּאֲבָנִים, זֶה שֵׁנִי. חָזַר וְטָחַן וְטָעַן, זֶה שְׁלִישִׁי. הָרִאשׁוֹן לַמְּנוֹרָה, וְהַשְּׁאָר לַמְּנָחוֹת. הַזַּיִת הַשְּׁלִישִׁי, עוֹטְנוֹ בְתוֹךְ הַבַּיִת עַד שֶׁיִּלְקֶה, וּמַעֲלֵהוּ וּמְנַגְּבוֹ בְרֹאשׁ הַגַּג, וְכוֹתֵשׁ וְנוֹתֵן לְתוֹךְ הַסַּל. רַבִּי יְהוּדָה אוֹמֵר, סְבִיבוֹת הַסַּל, זֶה רִאשׁוֹן. טָעַן בְּקוֹרָה, רַבִּי יְהוּדָה אוֹמֵר, בַּאֲבָנִים, זֶה שֵׁנִי. חָזַר וְטָחַן וְטָעַן, זֶה שְׁלִישִׁי. הָרִאשׁוֹן לַמְּנוֹרָה, וְהַשְּׁאָר לַמְּנָחוֹת:
There are three [periods of gathering in the] olives and each crop gives three kinds of oil. The first crop of olives is when the olives are picked from the top of the tree; they are pounded and put into the basket. Rabbi Judah says: around the basket. This gives the first oil. They are then pressed with the beam Rabbi Judah says: with stones. This gives the second oil. They are then ground and pressed again. This gives the third oil. The first [oil] is fit for the candlestick and the others for menahot. The second crop is when the olives at roof-level are picked from the tree; they are pounded and put into the basket. Rabbi Judah says: around the basket. This gives the first oil. They are then pressed with the beam Rabbi Judah says: with stones. This gives the second oil. They are then ground and pressed again. This gives the third oil. The first [oil] is fit for the candlestick and the others for menahot. The third crop is when the last olives of the tree are packed inside the house until they become overripe; they are then taken up and dried on the roof they are pounded and put into the basket. Rabbi Judah says: around the basket. This gives the first oil. They are then pressed with the beam Rabbi Judah says: with stones. This gives the second oil. They are then ground and pressed again. This gives the third oil. The first [oil] is fit for the candlestick and the others for menahot.