The word processor’s suggestion is correct, and the original wording is not natural. If you had not used “we imagine”, you could have used the infinitive: “We should say something on how to implement this” is fine. But it isn’t natural to use the infinitive directly after the verb “imagine”: we don’t say *“we imagine to implement this”, but instead “we imagine implementing this.”
In general, different verbs in English may be followed by other verbs in either the to-infinitive form or the -ing form. The identity of the first verb in the chain (in this case, imagine) is important for determining the form of the second verb in the chain. Some verbs have both as options, but others can only be used with one or the other. I don’t know a simple explanation for why the verb imagine is used with -ing forms instead of with to-infinitives, but that is why the word processor suggested changing your sentence.
A term for verbs that combine with other verbs is "catenative verbs" (from Latin catena meaning "chain"). You can use that as a search term to find more information about this topic. Here are links to two questions on this topic on the ELU site: How do I know when a verb should be followed by a gerund or an infinitive?, When should a verb be followed by a gerund instead of an infinitive? You can see that VonC's answer to the second describes "imagine" as a verb that must be followed by the -ing form.