The Hebrew text of Mal. 1:7 states,
ז מַגִּישִׁים עַל מִזְבְּחִי לֶחֶם מְגֹאָל וַאֲמַרְתֶּם בַּמֶּה גֵאַלְנוּךָ בֶּאֱמָרְכֶם שֻׁלְחַן יַהְוֶה נִבְזֶה הוּא
Although not one of the typical words translated into English by the verb “offer,” the Hifʿil participle מַגִּישִׁים appears to be suitably translated as “offer” in this particular context.1
The question thus remains, “What is לֶחֶם מְגֹאָל—‘polluted bread’?”
First, it cannot refer to the bread of the presence (לֶחֶם פָּנִים), a.k.a. “shewbread,” as that was never offered on the altar. By the way, when the prophet Malachi states, “The table of Yahveh is contemptible” (שֻׁלְחַן יַהְוֶה נִבְזֶה הוּא), “table” refers to the altar itself.2
“The table of Yahveh”—It is the altar, and so it said in Eze. 41:22 regarding the altar, “This is the table that is before Yahveh.”
שלחן יהוה - הוא המזבח וכן אמר ביחזקאל על המזבח: זה השלחן אשר לפני יהוה
There appears to be a parallel between Mal. 1:7 and 1:8 that provides the answer to the question of the identity of the לֶחֶם מְגֹאָל. In both verses, there is the presence of a conjugation of the verb נָגַשׁ:

More importantly, there is a parallelism between the “polluted bread” of Mal. 1:7 and the “lame” (עִוֵּר), “blind” (פִּסֵּחַ), and “sick” (חֹלֶה) of Mal. 1:8, thus equating the polluted bread with the lame, blind, and sick offering. Of course, this lame, blind, sick offering does not refer to a blind person (i.e., a human), but rather, lame, blind, and sick animals.
In Deu. 15:21, it is written,
21 And if there be any blemish therein, as if it be lame, or blind, or have any ill blemish, thou shalt not sacrifice it unto the LORD thy God. KJV, 1769
כא וְכִי יִהְיֶה בוֹ מוּם פִּסֵּחַ אוֹ עִוֵּר כֹּל מוּם רָע לֹא תִזְבָּחֶנּוּ לַיהְוֶה אֱלֹהֶֽיךָ
This verse mentions a sacrifice that is “lame” (פִּסֵּחַ) or “blind” (עִוֵּר), and it describes such a blemish as being רָע, literally “evil.”
In Lev. 21:6, it is written,
6 They shall be holy unto their God, and not profane the name of their God: for the offerings of the LORD made by fire, and the bread of their God, they do offer: therefore they shall be holy. KJV, 1769
ו קְדֹשִׁים יִהְיוּ לֵאלֹהֵיהֶם וְלֹא יְחַלְּלוּ שֵׁם אֱלֹהֵיהֶם כִּי אֶת אִשֵּׁי יַהְוֶה לֶחֶם אֱלֹהֵיהֶם הֵם מַקְרִיבִם וְהָיוּ קֹדֶשׁ
There are a couple facets worth noting. First, the priests either do or do not profane the name of their God on account of their offerings. If they offer the proper sacrifices, i.e., those without blemish, then they sanctify (i.e., do not profane) the name of their God, whereas if they offer blemished sacrifices, then they profane the name of their God, and thus despise it.
Next, the [animal] offerings to Yahveh made by fire are they themselves “the bread of their God” (לֶחֶם אֱלֹהֵיהֶם). This same notion is repeated elsewhere in the Torah.3
Regarding the Hebrew word לֶחֶם, Heinrich Friedrich Wilhelm Gesenius wrote,4

Therefore, in Mal. 1:7–8, it is not some literal bread offering that is the “polluted bread,” but rather, those blemished animal sacrifices that the priests were offering contrary to the Torah.
References
Gesenius, Heinrich Friedrich Wilhelm. Gesenius’s Hebrew and Chaldee Lexicon to the Old Testament Scriptures. Trans. Tregelles, Samuel Prideaux. London: Bagster, 1860.
Footnotes
1 cp. Amos 5:25: הַזְּבָחִים וּמִנְחָה הִגַּשְׁתֶּם לִי—“Have you offered Me sacrifices and offerings...?”
2 David Kimchi, commentary on Mal. 1:7
3 Lev. 3:11, 3:16, 21:6, 21:8, 21:17, 21:21–22, 22:25
4 p. 436