A relevant source that shows that prayers by non-Jews on behalf of Jews (to G-d, that is, not to their own deities) are not only appreciated but have a definite effect:
וְאָמַר רַבִּי אֶלְעָזָר אָמַר רַבִּי חֲנִינָא: לְעוֹלָם אַל תְּהִי בִּרְכַּת הֶדְיוֹט קַלָּה בְּעֵינֶיךָ, שֶׁהֲרֵי שְׁנֵי גְּדוֹלֵי הַדּוֹר בֵּרְכוּם שְׁנֵי הֶדְיוֹטוֹת, וְנִתְקַיְּימָה בָּהֶן, וְאֵלּוּ הֵן: דָּוִד וְדָנִיֵּאל. דָּוִד — דְּבָרְכֵיהּ אֲרַוְנָה, דִּכְתִיב: ״וַיֹּאמֶר אֲרַוְנָה אֶל הַמֶּלֶךְ וְגוֹ׳״. דָּנִיאֵל — דְּבָרְכֵיהּ דָּרְיָוֶשׁ, דִּכְתִיב: ״אֱלָהָךְ דִּי אַנְתְּ פָּלַח לֵיהּ בִּתְדִירָא הוּא יְשֵׁיזְבִינָּךְ״.
And Rabbi Elazar further said that Rabbi Ḥanina said: One should never regard the blessing of an ordinary person [hedyot]* as light in your eyes, as two of the great men of their generations received blessings from ordinary people and those blessings were fulfilled in them. And they were David and Daniel. David, for Araunah blessed him, as it is written: “And Araunah said to the king, May the Lord your God accept you” (II Samuel 24:23), and it was fulfilled. Daniel, for Darius blessed him, as it is written: “Your God Whom you serve continually, He will rescue you” (Daniel 6:17), and this too was fulfilled when Daniel was saved from the lions’ den.
(Talmud, Megillah 15a)
* Both Araunah and Darius were kings, actually, but relative to the spiritual stature of David and Daniel, they can well be called "ordinary people."