Using their logo implies that they are truly partners / customers of yours.
Is this the case?
It not, it is grossly misleading.
Otherwise, I would check with them, out of courtesy. They may not want their competitors knowing what software services they use. I don't believe you are legally obligated to do this, but it would certainly help to maintain a relationship with them by asking first.
Having worked in B2B for much of my career, I have seen this handled a variety of ways. Here's my perspective.
This is likely a highly ambiguous situation with important potential downside. Make one of these SIs angry and you jeopardize a big sale. Fail to capitalize on the publicity, lose traction. High severity/high ambiguity means it's a question for your CEO.
Factors to consider: how sensitive is your industry and these SIs to revealing technology providers? How many leads do you have in the hopper that will be swayed? How important is it to have the SIs mentioned on your website, vice perhaps having the name dropped "accidentally" in conversation with a new prospect? To what degree are these SI's "partners" vs. customers?
In most _sales_ contracts I've signed there has been language about use of the customer company logo and whether it can be revealed that we were selling to the customer. In the world of web APIs, where ecosystem enablement is important and it is truly more a partnership, many companies are more promiscuous with letting their name be used and they have simple guidelines for doing so published on their website. Happy to jump on a call and help you work through this in more detail.