Learn English – “In” or “At” sole discretion

They both carry the same basic sense of discernment or judgement which can be considered synonyms of the word.

Discretion derives from the Latin stem discrēt- meaning to separate or to divide - and therefore to discern (which is also derived from the common stem cernĕre (to separate)) - giving rise to two words in English which essentially mean the same (discreet and discrete). Thus, to be discrete means to separate or divide, which means to be discreet or to exercise discretion (discernment). The spelling discreet tends to be used more in a moral context with the second spelling discrete now more common in other contexts.

'At its discretion' is right usage, but in the same sentence first you have used the pronoun 'it' for 'Company A' and later on you have used the pronoun 'they', which doesn't seem correct. People may argue that in this case 'they' is singular pronoun, however, I think that from consistency point of view it's not advisable to use two different pronouns for the same thing in one sentence.

The word 'harms' is perfectly OK, too, because 'Company A' is singular.