Alita had not touched Chris ever since she arrived as she felt bad for her but after thinking of what Octavia did, she came to a conclusion and she decided to deal with the situation accordingly.
Since Chris was bullied because she was a mere servant, Alita decided to change that. Chris had carried her child and lost it and this wasn't her fault and for that, she didn't deserve to be a mere servant and bedwarmer.
Even though she wasn't going to be reckless and make her a wife, she can still make Chris a concubine and this status was much better than her original one.
So, on that night when having dinner which was by herself as in this world rules were followed seriously and she didn't want to make her people nervous for no reason.