with strings

Having one or more special conditions, restrictions, obligations, or arrangements that must be met. Members of the majority party are willing to allow the bill to pass, but with strings. He was willing to give a hefty campaign donation, with strings: that his company's interests be put before others during legislative debates.

with strings

with strings attached

You can say that an offer is with strings or with strings attached if accepting it requires you to do a particular thing or give something in return. We cannot accept donations with strings attached. More often than not, aid comes with strings that bind the recipient to unfair relationships in the international market.