Basically, it depends on your approach, and which critical trends you have chosen (genetic criticism, historical criticism, formalism, psychoanalytic criticism etc.).
The most popular definition of the rhyme is "correspondence of sound between words or the endings of words, especially when these are used at the ends of lines of poetry." So, your example does not fit the definition, and it looks as it is not the rhyme from your or our point of view.
Rhyme is the repetition of similar sounds in two or more words. In poetry these words are usually at the end of a line and help create a certain rhythm. There is the perfect opportunities of looking for the rhyme online (for instance, http://www.rhymezone.com) So, the main aspect of the rhyme is related to phonetics.
However, here is the poetry written by the poet who has his own language background. Eliot was born in 1888, more than hundred years ago, and even changed his citizenship. If you would read Shakespeare's poetry, you will notice that the meaning of the words changed during several hundred years, probably it happened to the pronunciation as well (there are no records how Shakespeare pronounced different words). I think it is the rhyme because Eliot could pronounce words in different way then you or me pronounce them today. It could be his dialect or even idiolect ("The speech habits peculiar to a particular person").
Moreover, the essence of the poetry is to sound, not to stay in the written form. Thus, it is the rhyme, and these words ("charm" and "warm") should be read as they sound the similar way. Of course there are opinions claiming that the rhyme is not necessary part of the modern poetry, perhaps they are right, but the text of literature should be interpreted in the sense of author's way (historical approach), and, when Eliot wrote this piece of poetry, the rhyme was more important than today.