Shmos 15:26 –  And He said, if you hearken to the voice of the Lord, your God, and you do what is proper in His eyes, and you listen closely to His commandments and observe all His statutes, all the sicknesses that I have visited upon Egypt I will not visit upon you, for I, the Lord, heal you.

Gemora – Sanhedrin 90a: One who whispers on a wound and says “All the sicknesses that I have visited upon Egypt I will not visit upon you” has no portion in the world to come.

Torah Temimah Colloquial Translation of Comment #44:
The Gemora in our chapter (101a) notes that Rabbi Yochanan states that the Gemora is speaking of a situation where someone spits; this being forbidden because it is not proper to mention God’s name while spitting. Rashi there explains that it is the way of whisperers to spit prior to their whisper. In other words, based on Rashi, first they spit and then they say the verse with God’s name in it, “For I, the Lord, heal you.” However, the Tur in Yoreh Deah Section 179 states that the custom of whisperers is to say the verse first [with God’s name in it] and then spit.

Thus, according to the Tur, there would be support for the custom of those who spit during the Alenu prayer before they mention God’s name. The only prohibition being the opposite, namely to mention God’s name first and then spit. This would be prohibited because it would appear as though one is disparaging God’s name. But, if one follows the opinion of Rashi that spitting even before mentioning God’s name is also forbidden, then the custom of spitting during Alenu would be difficult [to support].  

That which the Tur writes in the above noted section that in those instances where it is obvious that one intends to honor God in spitting [as in the Alenu prayer] then it would be permitted, that doesn’t appear to be applicable. The case brought in our Gemora of one who is whispering upon a wound also does not mean to disrespect God, but rather the opposite is true in that he is honoring God by saying a verse that he hopes will cause healing. Nevertheless, the Gemora makes it clear that even in such a case it is still prohibited because it is just not honorable to mention God’s name in connection with spitting.

In summary, if one follows Rashi’s understanding of the Gemora, it is better to not spit during the Alenu prayer. This is how I have seen great men of our generation acting and I have followed their example.

 Editor’s Note: The bottom line is that the Torah Temimah is pointing out that it seems inappropriate to spit during prayers, no matter what.