Just in case you don't tweet, I'd better explain what's going on here. The Invisible Woman has tweeted her own comment, *speechless with delight* (the asterisks mean that she isn't saying it, it's an action, state or feeling). The rest of the tweet is from Corrie Corfield, which Invisible Woman has repeated - RT means 'retweet'. Now, retweets may just consist of the original tweet, repeated in order to bring your followers' attention to it, or they may, as here, have some comment added. Either way, the RT means that the tweet is quoted as it originally was. You might modify the tweet slightly, by removing some content to make it fit or editing it somehow, and then the normal rules apply (preserve the original intent) and you use MT ('modified tweet'). IW uses RT, so we can assume the tweet is verbatim.
Corrie replies, however, to the effect that she didn't in fact put it like that, and I checked her timeline and it appears that none of the tweet is hers. RT isn't really appropriate here, then. She did, however, say something to this effect, so the original intent is preserved. Should IW have used MT? I would say not, actually, because modified tweets tend to be edited only slightly. It's similar to quoting or paraphrasing academic authors: if you put it in quotation marks, the words are the original author's. You can edit them very slightly, by missing out some words that are not needed for your purposes, or adding in a clarifying bracketed phrase to replace a pronoun that's not clear in context, but no more than this. Any more serious changes and what you're doing is paraphrasing, not quoting. Retweeting is quoting, and MTing is quoting with minor editorial changes. We need a convention to indicate paraphrasing that allows us to use it in 140 characters or less.
It's similar to the use of 'like' for reported speech, maybe. If you say (1) below, we can reasonably safely assume that those were more or less her words. If you say (2), we don't have that security. (3) is more like (2) than (1) in this respect, in that it conveys her message but not necessarily her words. This is an oversimplification, but perhaps this is how RT and MT will come to be used.
(1) Phyllis said "I really hate Bertha".
(2) Phyllis says she really hates Bertha.
(3) Phyllis was like "I really hate Bertha".