The Nigerian courted controversy on transfer deadline when he travelled to QPR with a transfer in mind - only to end up returning to The Hawthorns to fight for his place.
Baggies fans reacted with mixed levels of disapproval initially, but Odemwingie received an improved reception from the away fans at last weekend's 1-0 defeat at Chelsea.
Clarke said: "Everyone knows the Peter incident happened but it's past for us and we have all moved on from it, and I look forward to his contribution for the rest of the season.
"Peter and I have a good relationship, coach-player excellent relationship. I think he is a good talent and I look forward to him making a good contribution for the rest of the season.
"People have to move on. We have moved on from it and the less we talk about it the more likely we are to move on completely from it.
"Am I keen to see home fans put things in the past? I would like to think so and if he plays and scores goals they will give him a good reception."
West Brom host Swansea on Saturday and Odemwingie may be handed a start sooner rather than later, given that Republic of Ireland star Shane Long is struggling with an ankle problem.
Clarke said of Long: "The one unfortunate thing for us is that Shane Long, who played last week with a bad ankle, has aggravated his ankle through the week.
"He trained Monday, Tuesday, unfortunately he didn't train today, is doubtful to train tomorrow and is doubtful for the weekend as well so that is a bitter loss for us."