This is a controversial issue. If you look at older siddurim, like the one of R' Yaakov Emden, who, besides his other talents, was an exceptional authority on grammar, you can find the על גבי version in plural. This was criticised by Isaac Satanow, who suggested to write it in the singular על גב form. He argued that in Yechezkeil 43:13 it is written in the singular form, and it should be written this way:
וְאֵ֨לֶּה מִדּ֤וֹת הַמִּזְבֵּ֨חַ֙ בָּֽאַמּ֔וֹת אַמָּ֥ה אַמָּ֖ה וָטֹ֑פַח וְחֵ֨יק הָֽאַמָּ֜ה וְאַמָּה־רֹ֗חַב וּגְבוּלָ֨הּ אֶל־שְׂפָתָ֤הּ סָבִיב֙ זֶ֣רֶת הָֽאֶחָ֔ד וְזֶ֖ה גַּ֥ב הַמִּזְבֵּֽחַ׃
And these are the measures of the altar by cubits, the cubit is a cubit and a handbreadth, the bottom shall be a cubit, and the breadth a cubit, and the border thereof by the edge thereof round about a span; and this shall be the base of the altar.
R' Wolf Heidenheim followed Satanow's opinion in his extremely influential prayer book. However, popular editions like Artscroll and Eshkol, or German siddurim (e.g. Sefas Yisroel p. 9) rejected this and reverted to the older version.
As Kouty kindly pointed out, the Mishnah uses the plural form (see Pesachim 5:8, 10) even in other cases when the object is in singular (see על גבי בהמה in Menachot 1:2). This illustrates the conflict between the orthography of the Tanakh and the later works of the Sages. Satanow propagated the former, even in case of prayers that were originally composed in the language of the Sages (לשון חז"ל).