You need a very thorough weeding because unfortunately, your ground cover plants will not out compete the grass, more the other way around, except for the ivy, which in itself is difficult to control. If you find its impossible to extract the grass roots without damaging roots of plants you want to keep, its probably best to wait till Fall (whenever that is where you are), then dig up the plants as well, extract all the grass roots, keep the plants covered or sit them in containers with the roots in water at the bottom temporarily, dig the area over to remove any remaining grass and replant the plants. Water in well. Best completed in a day if possible.
If that sounds like too much work, then you can always try spraying the grass with a weedkiller like glyphosate, but you'd need to protect the other plants around it from the spray or it will kill those too. Some weedkillers that work on grass might be available in a paint on form - I've never found them very effective, but maybe you have a bigger range of this type of weedkiller where you are than we do here in the UK.