If you're trying to remove items from items that don't have a thumbnail, it's better to do it on the backend when you get them.
this.items = this.items.filter(function(item) {
return (item &&
item._embedded &&
item._embedded['wp:featuredmedia'] &&
item._embedded['wp:featuredmedia'][0] &&
item._embedded['wp:featuredmedia'][0].media_details &&
item._embedded['wp:featuredmedia'][0].media_details.sizes &&
item._embedded['wp:featuredmedia'][0].media_details.sizes.thumbnail &&
item._embedded['wp:featuredmedia'][0].media_details.sizes.thumbnail.source_url);
});
If you want to get every item, thumbnail or no, but hide the thumbnail if it doesn't exist, use *ngIf on your img tag.
<ion-card *ngFor="let item of items">
<img *ngIf="item &&
item._embedded &&
item._embedded['wp:featuredmedia'] &&
item._embedded['wp:featuredmedia'][0] &&
item._embedded['wp:featuredmedia'][0].media_details &&
item._embedded['wp:featuredmedia'][0].media_details.sizes &&
item._embedded['wp:featuredmedia'][0].media_details.sizes.thumbnail &&
item._embedded['wp:featuredmedia'][0].media_details.sizes.thumbnail.source_url"
src="{{item._embedded['wp:featuredmedia'][0].media_details.sizes.thumbnail.source_url}}"/>
</ion-card>
Note: The reason you should check each layer of the object is because if any one of them is missing, you'll get a TypeError saying "could not find property X of undefined".